Core blocks for Hecke algebras of type B and sign sequences

We consider the core blocks corresponding to the Hecke algebras of type B over a field of arbitrary characteristic. To each core block, we associate two non-negative integers which determine the indexing of the Specht modules and simple modules in the block, the weight of the block, the multicharge of the algebra (up to a shift) and the block decomposition matrix

Schurian‐finiteness of blocks of type AAA Hecke algebras

For any algebra over an algebraically closed field , we say that an -module is Schurian ifEnd() ≅ . We say that is Schurian-finite if there are only finitely many isomorphism classes of Schurian -modules, and Schurian-infinite otherwise. By work of Demonet, Iyama and Jasso, it is known that Schurian-finiteness is equivalent to -tilting-finiteness, so thatwemay drawon a wealth of known results in the subject. We prove that for the type Hecke algebras with quantum characteristic ⩾ 3, all blocks of weight at least 2 are Schurianinfinite in any characteristic. Weight 0 and 1 blocks are known by results of Erdmann and Nakano to be representation finite, and are therefore Schurian-finite. This means that blocks oftype Hecke algebras (when ⩾ 3) are Schurian-infinite if and only if they have wild representation type if and only if the module category has finitely many wide subcategories. Along theway, we also prove a graded version of the Scopes equivalence, which is likely to be of independent interest.journal articl

Carter-Payne homomorphisms and Jantzen filtrations

We prove a q-analogue of the Carter-Payne theorem in the case where the differences between the parts of the partitions are sufficiently large. We identify a layer of the Jantzen filtration which contains the image of these Carter-Payne homomorphisms and we show how these homomorphisms compose.Comment: 30 page

Graded decomposition numbers of Ariki-Koike algebras for blocks of small weight

We present some blocks of Ariki-Koike algebras H_{n,r} for which the decomposition matrices are independent of the characteristic of the underlying field. We complete the description of the graded decomposition numbers for blocks of Ariki-Koike algebras of weight at most two, which consists of analysing the indecomposable core blocks at level r = 3, and give a closed formula for the decomposition numbers in this case

Effect of angiotensin-converting enzyme inhibitor and angiotensin receptor blocker initiation on organ support-free days in patients hospitalized with COVID-19

IMPORTANCE Overactivation of the renin-angiotensin system (RAS) may contribute to poor clinical outcomes in patients with COVID-19. Objective To determine whether angiotensin-converting enzyme (ACE) inhibitor or angiotensin receptor blocker (ARB) initiation improves outcomes in patients hospitalized for COVID-19. DESIGN, SETTING, AND PARTICIPANTS In an ongoing, adaptive platform randomized clinical trial, 721 critically ill and 58 non–critically ill hospitalized adults were randomized to receive an RAS inhibitor or control between March 16, 2021, and February 25, 2022, at 69 sites in 7 countries (final follow-up on June 1, 2022). INTERVENTIONS Patients were randomized to receive open-label initiation of an ACE inhibitor (n = 257), ARB (n = 248), ARB in combination with DMX-200 (a chemokine receptor-2 inhibitor; n = 10), or no RAS inhibitor (control; n = 264) for up to 10 days. MAIN OUTCOMES AND MEASURES The primary outcome was organ support–free days, a composite of hospital survival and days alive without cardiovascular or respiratory organ support through 21 days. The primary analysis was a bayesian cumulative logistic model. Odds ratios (ORs) greater than 1 represent improved outcomes. RESULTS On February 25, 2022, enrollment was discontinued due to safety concerns. Among 679 critically ill patients with available primary outcome data, the median age was 56 years and 239 participants (35.2%) were women. Median (IQR) organ support–free days among critically ill patients was 10 (–1 to 16) in the ACE inhibitor group (n = 231), 8 (–1 to 17) in the ARB group (n = 217), and 12 (0 to 17) in the control group (n = 231) (median adjusted odds ratios of 0.77 [95% bayesian credible interval, 0.58-1.06] for improvement for ACE inhibitor and 0.76 [95% credible interval, 0.56-1.05] for ARB compared with control). The posterior probabilities that ACE inhibitors and ARBs worsened organ support–free days compared with control were 94.9% and 95.4%, respectively. Hospital survival occurred in 166 of 231 critically ill participants (71.9%) in the ACE inhibitor group, 152 of 217 (70.0%) in the ARB group, and 182 of 231 (78.8%) in the control group (posterior probabilities that ACE inhibitor and ARB worsened hospital survival compared with control were 95.3% and 98.1%, respectively). CONCLUSIONS AND RELEVANCE In this trial, among critically ill adults with COVID-19, initiation of an ACE inhibitor or ARB did not improve, and likely worsened, clinical outcomes. TRIAL REGISTRATION ClinicalTrials.gov Identifier: NCT0273570

Some reducible Specht modules for Iwahori–Hecke algebras of type A with q=−1

The reducibility of the Specht modules for the Iwahori–Hecke algebras in type A is still open in the case where the defining parameter q equals−1. We prove the reducibility of a large class of Specht modules for these algebras.

Rouquier blocks

This paper investigates the Rouquier blocks of the Hecke algebras of the symmetric groups and the Rouquier blocks of the q-Schur algebras. We first give an algorithm for computing the decomposition numbers of these blocks in the ``abelian defect group case'' and then use this algorithm to explicitly compute the decomposition numbers in a Rouquier block. For fields of characteristic zero, or when q=1 these results are known; significantly, our results also hold for fields of positive characteristic with q?1. We also discuss the Rouquier blocks in the ``non–abelian defect group'' case. Finally, we apply these results to show that certain Specht modules are irreducible

Large-dimensional homomorphism spaces between Weyl modules and Specht modules

We give a family of pairs of Weyl modules for the q-Schur algebras for which the corresponding homomorphism space is at least 2-dimensional. Using this result we show that for any field F and any quantum characteristic, there exist arbitrarily large homomorphism spaces between pairs of Weyl modules

Schurian‐finiteness of blocks of type Hecke algebras

For any algebra over an algebraically closed field , we say that an -module is Schurian ifEnd() ≅ . We say that is Schurian-finite if there are only finitely many isomorphism classes of Schurian -modules, and Schurian-infinite otherwise. By work of Demonet, Iyama and Jasso, it is known that Schurian-finiteness is equivalent to -tilting-finiteness, so thatwemay drawon a wealth of known results in the subject. We prove that for the type Hecke algebras with quantum characteristic ⩾ 3, all blocks of weight at least 2 are Schurianinfinite in any characteristic. Weight 0 and 1 blocks are known by results of Erdmann and Nakano to be representation finite, and are therefore Schurian-finite. This means that blocks oftype Hecke algebras (when ⩾ 3) are Schurian-infinite if and only if they have wild representation type if and only if the module category has finitely many wide subcategories. Along theway, we also prove a graded version of the Scopes equivalence, which is likely to be of independent interest