Cyclotomic Carter-Payne homomorphisms

We construct a new family of homomorphisms between (graded) Specht modules of the quiver Hecke algebras of type A. These maps have many similarities with the homomorphisms constructed by Carter and Payne in the special case of the symmetric groups, although the maps that we obtain are both more and less general than these.Comment: This paper has been updated. The formula for the degree shift in Theorem 3.28 has been corrected and Examples 3.31 and 3.36 have been changed accordingl

Blocks of cyclotomic Hecke algebras

This paper classifies the blocks of the cyclotomic Hecke algebras of type G(r,1,n) over an arbitrary field. Rather than working with the Hecke algebras directly we work instead with the cyclotomic Schur algebras. The advantage of these algebras is that the cyclotomic Jantzen sum formula gives an easy combinatorial characterization of the blocks of the cyclotomic Schur algebras. We obtain an explicit description of the blocks by analyzing the combinatorics of `Jantzen equivalence'. We remark that a proof of the classification of the blocks of the cyclotomic Hecke algebras was announced in 1999. Unfortunately, Cox has discovered that this previous proof is incomplete.Comment: Final version. To appear in Advances in Mathematic

Decomposition numbers for Rouquier blocks of Ariki-Koike algebras I

Let $\mathcal{H}$ denote an Ariki-Koike algebra over a field of characteristic $p\geq 0$. For each $r$-multipartition ${\bf \lambda}$ of $n$, we define a $\mathcal{H}$-module $S^{{\bf \lambda}}$ and for each Kleshchev $r$-multipartition ${\bf \mu}$ of $n$, we define an irreducible $\mathcal{H}$-module $D^{{\bf \mu}}$. Given a multipartition ${\bf \lambda}$ and a Kleshchev multipartition ${\bf \mu}$ both lying in a Rouquier block and which have a common multicore, we give a closed formula for the graded decomposition number $[S^{{\bf \lambda}}:D^{{\bf \mu}}]_v$ when $p=0$.Comment: 25 page

Rouquier blocks for Ariki-Koike algebras

The Rouquier blocks, also known as the RoCK blocks, are important blocks of the symmetric groups algebras and the Hecke algebras of type A, with the partitions labelling the Specht modules that belong to these blocks having a particular abacus configuration. We generalise the definition of Rouquier blocks to the Ariki-Koike algebras, where the Specht modules are indexed by multipartitions, and explore the properties of these blocksComment: 19 page

On bases of some simple modules of symmetric groups and Hecke algebras

We consider simple modules for a Hecke algebra with a parameter of quantum characteristic e. Equivalently, we consider simple modules Dλ, labelled by e-restricted partitions λ of n, for a cyclotomic KLR algebra RΛ0nRnΛ0 over a field of characteristic p ≥ 0, with mild restrictions on p. If all parts of λ are at most 2, we identify a set DStde,p(λ) of standard λ-tableaux, which is defined combinatorially and naturally labels a basis of Dλ. In particular, we prove that the q-character of Dλ can be described in terms of DStde,p(λ). We show that a certain natural approach to constructing a basis of an arbitrary Dλ does not work in general, giving a counterexample to a conjecture of Mathas

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

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

Decomposition numbers for Rouquier blocks of Ariki-Koike algebras I

Let H=Hr,n​(q,Q) denote an Ariki–Koike algebra over a field of characteristic p≥0. For each r-multipartition λ of n, there exists a H-module Sλ and for each Kleshchev r-multipartition μ of n, there exists an irreducible H-module Dμ. Given a multipartition λ and a Kleshchev multipartition μ both lying in a Rouquier block such that λ and μ have the same multicore, we give a closed formula for the graded decomposition number [Sλ:Dμ]v​ when p=0 or when each component of μ has fewer than p removable e-rim hooks