The Robinson-Schensted Correspondence and A2A_2-web Bases

We study natural bases for two constructions of the irreducible representation of the symmetric group corresponding to $[n,n,n]$: the {\em reduced web} basis associated to Kuperberg's combinatorial description of the spider category; and the {\em left cell basis} for the left cell construction of Kazhdan and Lusztig. In the case of $[n,n]$, the spider category is the Temperley-Lieb category; reduced webs correspond to planar matchings, which are equivalent to left cell bases. This paper compares the images of these bases under classical maps: the {\em Robinson-Schensted algorithm} between permutations and Young tableaux and {\em Khovanov-Kuperberg's bijection} between Young tableaux and reduced webs. One main result uses Vogan's generalized $\tau$-invariant to uncover a close structural relationship between the web basis and the left cell basis. Intuitively, generalized $\tau$-invariants refine the data of the inversion set of a permutation. We define generalized $\tau$-invariants intrinsically for Kazhdan-Lusztig left cell basis elements and for webs. We then show that the generalized $\tau$-invariant is preserved by these classical maps. Thus, our result allows one to interpret Khovanov-Kuperberg's bijection as an analogue of the Robinson-Schensted correspondence. Despite all of this, our second main result proves that the reduced web and left cell bases are inequivalent; that is, these bijections are not $S_{3n}$-equivariant maps.Comment: 34 pages, 23 figures, minor corrections and revisions in version

The Robinson-Schensted Correspondence and A2-Web Bases

We study natural bases for two constructions of the irreducible representation of the symmetric group corresponding to [n; n; n]: the reduced web basis associated to Kuperberg\u27s combinatorial description of the spider category; and the left cell basis for the left cell construction of Kazhdan and Lusztig. In the case of [n; n], the spider category is the Temperley-Lieb category; reduced webs correspond to planar matchings, which are equivalent to left cell bases. This paper compares the image of these bases under classical maps: the Robinson-Schensted algorithm between permutations and Young tableaux and Khovanov-Kuperberg\u27s bijection between Young tableaux and reduced webs. One main result uses Vogan\u27s generalized T-invariant to uncover a close structural relationship between the web basis and the left cell basis. Intuitively, generalized T-invariants refine the data of the inversion set of a permutation. We define generalized T-invariants intrinsically for Kazhdan-Lusztig left cell basis elements and for webs. We then show that the generalized T-invariant is preserved by these classical maps. Thus, our result allows one to interpret Khovanov-Kuperberg\u27s bijection as an analogue of the Robinson-Schensted correspondence. Despite all of this, our second main result proves that the reduced web and left cell bases are inequivalent; that is, these bijections are not S3n-equivariant maps

The Robinson-Schensted Correspondence and A\u3csub\u3e2\u3c/sub\u3e-web Bases

We study natural bases for two constructions of the irreducible representation of the symmetric group corresponding to [n, n, n]: the reduced web basis associated to Kuperberg’s combinatorial description of the spider category; and the left cell basis for the left cell construction of Kazhdan and Lusztig. In the case of [n, n], the spider category is the Temperley-Lieb category; reduced webs correspond to planar matchings, which are equivalent to left cell bases. This paper compares the image of these bases under classical maps: the Robinson–Schensted algorithm between permutations and Young tableaux and Khovanov–Kuperberg’s bijection between Young tableaux and reduced webs. One main result uses Vogan’s generalized τ-invariant to uncover a close structural relationship between the web basis and the left cell basis. Intuitively, generalized τ-invariants refine the data of the inversion set of a permutation. We define generalized τ-invariants intrinsically for Kazhdan–Lusztig left cell basis elements and for webs. We then show that the generalized τ-invariant is preserved by these classical maps. Thus, our result allows one to interpret Khovanov–Kuperberg’s bijection as an analogue of the Robinson–Schensted correspondence. Despite all of this, our second main result proves that the reduced web and left cell bases are inequivalent; that is, these bijections are not S3n-equivariant maps

We\u27re Bringing Spacers Back: Secondary Processing at Utah State University Archives

Processing can be an iterative process but finding time and resources to re-evaluate existing collections is difficult, especially with backlogs and new acquisitions. However, secondary processing can greatly improve access, discoverability, and the physical condition of the materials. This session examines the process in which Utah State University Archives, as part of a larger cataloging project to modernize University began and carried out an evaluation of collections for secondary processing and rehousing

It\u27s Time for an EAD Glow Up! How to Make Finding Aids More Attractive to Users

USU Libraries investigated discoverability of local Encoded Archival Description (EAD) finding aids using different levels of description. The research team created two dueling finding aids of the same collection; one with an MPLP stripped down box level inventory, and the other with a more robust item level of description. Both finding aids were posted online simultaneously and left untouched for over a year. The data was then pulled and assessed for each collection with the more \u27glowed up\u27 item level finding aid being, on average, 61x more discoverable than the finding aids described at the file level. Presenters will discuss the methodology of the project, what tools were used to conduct the research and analyze results, how these results have informed internal metadata practices, and next steps to expand this research by \u27retouching\u27 other existing legacy finding aids

University Treasure – Collections of Secrets: How Utah State University Libraries Modernized Their University Archives

Starting in 2018, Utah State University Libraries undertook a largescale cataloging project to modernize the University Archives. Before 2018 the University Archives was largely inaccessible to patrons with only 2% of collections having online finding aids and no existing electronic shelf list inventory. Using a workflow-driven approach, a team of catalogers, archivists, and student technicians embarked on a four-phase journey to inventory over 21,000 items, create EAD finding aids and MARC catalog records for over 2700 unique collections, and ingesting all collections into the Library’s newly implemented archival management system. Presenters will discuss the process developed, tools used, and outcomes of the project

The Robinson―Schensted Correspondence and A2A_2-webs

The $A_2$-spider category encodes the representation theory of the $sl_3$ quantum group. Kuperberg (1996) introduced a combinatorial version of this category, wherein morphisms are represented by planar graphs called $\textit{webs}$ and the subset of $\textit{reduced webs}$ forms bases for morphism spaces. A great deal of recent interest has focused on the combinatorics of invariant webs for tensors powers of $V^+$, the standard representation of the quantum group. In particular, the invariant webs for the 3$n$th tensor power of $V^+$ correspond bijectively to $[n,n,n]$ standard Young tableaux. Kuperberg originally defined this map in terms of a graphical algorithm, and subsequent papers of Khovanov–Kuperberg (1999) and Tymoczko (2012) introduce algorithms for computing the inverse. The main result of this paper is a redefinition of Kuperberg's map through the representation theory of the symmetric group. In the classical limit, the space of invariant webs carries a symmetric group action. We use this structure in conjunction with Vogan's generalized tau-invariant and Kazhdan–Lusztig theory to show that Kuperberg's map is a direct analogue of the Robinson–Schensted correspondence

The Revised DACS Principles in Action: Applying Modern Practice to Legacy Description

Since SAA revised DACS\u27s archival description principles from 8 concepts into 11 reworked value statements in 2019, archivists have wondered how to incorporate the revised principles into existing description practices. Archivists from BYU and USU libraries have undertaken large projects on legacy collections informed by these principles. We invite attendees to learn from our experiences in implementing current DACS principles while grappling with less-than-ideal records. BYU will describe a project to revise the description of a significant collection of Mesoamerican materials after discovering the finding aid had serious problems introduced by previous revisions by archivists. USU will describe an undertaking to create over 2,500 University Archives collection descriptions from a shelf list and revising based on the new DACS principles. This joint session will demonstrate straightforward ways that two academic libraries have incorporated the DACS principles into archivists\u27 day-to-day work

Familiar eyes are smiling: On the role of familiarity in the perception of facial affect

Abstract Quickly and accurately perceiving others' facial affect is paramount for successful social interaction. This work investigates the role of familiarity in helping us to interpret others' facial emotions. In Experiments 1 and 2, participants viewed several faces, some familiar and some novel, and judged how happy each face appeared. As predicted, results showed that familiar faces were perceived as happier than were novel faces. In Experiment 3, participants again viewed several faces, some familiar and some not, and rated the perceived anger or happiness of these faces. As expected, familiar faces were perceived as happier and less angry than were novel faces. Thus, these results suggest that familiarity is one cue we use to interpret the facial affect of others

Dipeptidyl peptidase-1 inhibition in patients hospitalised with COVID-19: a multicentre, double-blind, randomised, parallel-group, placebo-controlled trial

Background Neutrophil serine proteases are involved in the pathogenesis of COVID-19 and increased serine protease activity has been reported in severe and fatal infection. We investigated whether brensocatib, an inhibitor of dipeptidyl peptidase-1 (DPP-1; an enzyme responsible for the activation of neutrophil serine proteases), would improve outcomes in patients hospitalised with COVID-19. Methods In a multicentre, double-blind, randomised, parallel-group, placebo-controlled trial, across 14 hospitals in the UK, patients aged 16 years and older who were hospitalised with COVID-19 and had at least one risk factor for severe disease were randomly assigned 1:1, within 96 h of hospital admission, to once-daily brensocatib 25 mg or placebo orally for 28 days. Patients were randomly assigned via a central web-based randomisation system (TruST). Randomisation was stratified by site and age (65 years or ≥65 years), and within each stratum, blocks were of random sizes of two, four, or six patients. Participants in both groups continued to receive other therapies required to manage their condition. Participants, study staff, and investigators were masked to the study assignment. The primary outcome was the 7-point WHO ordinal scale for clinical status at day 29 after random assignment. The intention-to-treat population included all patients who were randomly assigned and met the enrolment criteria. The safety population included all participants who received at least one dose of study medication. This study was registered with the ISRCTN registry, ISRCTN30564012. Findings Between June 5, 2020, and Jan 25, 2021, 406 patients were randomly assigned to brensocatib or placebo; 192 (47·3%) to the brensocatib group and 214 (52·7%) to the placebo group. Two participants were excluded after being randomly assigned in the brensocatib group (214 patients included in the placebo group and 190 included in the brensocatib group in the intention-to-treat population). Primary outcome data was unavailable for six patients (three in the brensocatib group and three in the placebo group). Patients in the brensocatib group had worse clinical status at day 29 after being randomly assigned than those in the placebo group (adjusted odds ratio 0·72 [95% CI 0·57–0·92]). Prespecified subgroup analyses of the primary outcome supported the primary results. 185 participants reported at least one adverse event; 99 (46%) in the placebo group and 86 (45%) in the brensocatib group. The most common adverse events were gastrointestinal disorders and infections. One death in the placebo group was judged as possibly related to study drug. Interpretation Brensocatib treatment did not improve clinical status at day 29 in patients hospitalised with COVID-19