scholarly journals Drinfeld Hecke algebras for symmetric groups in positive characteristic

2021 ◽  
pp. 1-17
Author(s):  
N. Krawzik ◽  
A. V. Shepler
Keyword(s):  
Positive Characteristic ◽  
Hecke Algebras ◽  
Symmetric Groups

scholarly journals Dominant and global dimension of blocks of quantised Schur algebras

2021 ◽  
Author(s):  
Ming Fang ◽  
Wei Hu ◽  
Steffen Koenig
Keyword(s):  
Hecke Algebras ◽  
Symmetric Groups ◽  
Global Dimension ◽  
Group Algebras ◽  
Dominant Dimension ◽  
Schur Algebras ◽  
Homological Dimensions ◽  
Weyl Duality

AbstractGroup algebras of symmetric groups and their Hecke algebras are in Schur-Weyl duality with classical and quantised Schur algebras, respectively. Two homological dimensions, the dominant dimension and the global dimension, of the indecomposable summands (blocks) of these Schur algebras S(n, r) and $$S_q(n,r)$$ S q ( n , r ) with $$n \geqslant r$$ n ⩾ r are determined explicitly, using a result on derived invariance in Fang, Hu and Koenig (J Reine Angew Math 770:59–85, 2021).

scholarly journals ON BASES OF SOME SIMPLE MODULES OF SYMMETRIC GROUPS AND HECKE ALGEBRAS

2017 ◽  
Vol 23 (3) ◽  
pp. 631-669 ◽  
Author(s):  
M. DE BOECK ◽  
A. EVSEEV ◽  
S. LYLE ◽  
L. SPEYER
Keyword(s):  
Hecke Algebras ◽  
Symmetric Groups ◽  
Simple Modules

scholarly journals Springer correspondence for the split symmetric pair in type

2018 ◽  
Vol 154 (11) ◽  
pp. 2403-2425 ◽  
Author(s):  
Tsao-Hsien Chen ◽  
Kari Vilonen ◽  
Ting Xue
Keyword(s):  
Fourier Transform ◽  
Hecke Algebras ◽  
Symmetric Groups ◽  
Irreducible Representations ◽  
Symmetric Pair ◽  
Parabolic Induction ◽  
Hessenberg Varieties ◽  
Nearby Cycle ◽  
Springer Correspondence

In this paper we establish Springer correspondence for the symmetric pair $(\text{SL}(N),\text{SO}(N))$ using Fourier transform, parabolic induction functor, and a nearby cycle sheaf construction. As an application of our results we see that the cohomology of Hessenberg varieties can be expressed in terms of irreducible representations of Hecke algebras of symmetric groups at $q=-1$. Conversely, we see that the irreducible representations of Hecke algebras of symmetric groups at $q=-1$ arise in geometry.

scholarly journals DIAGRAM ALGEBRAS, DOMINANCE TRIANGULARITY AND SKEW CELL MODULES

2017 ◽  
Vol 104 (1) ◽  
pp. 13-36 ◽  
Author(s):  
CHRISTOPHER BOWMAN ◽  
JOHN ENYANG ◽  
FREDERICK GOODMAN
Keyword(s):  
Transition Matrix ◽  
Hecke Algebras ◽  
Symmetric Groups ◽  
Specht Modules ◽  
Diagram Algebras ◽  
Cell Modules ◽  
Abstract Framework

We present an abstract framework for the axiomatic study of diagram algebras. Algebras that fit this framework possess analogues of both the Murphy and seminormal bases of the Hecke algebras of the symmetric groups. We show that the transition matrix between these bases is dominance unitriangular. We construct analogues of the skew Specht modules in this setting. This allows us to propose a natural tableaux theoretic framework in which to study the infamous Kronecker problem.

scholarly journals Cohomological Invariants in Positive Characteristic

2021 ◽  
Author(s):  
Burt Totaro
Keyword(s):  
Positive Characteristic ◽  
Differential Forms ◽  
Symmetric Groups ◽  
Characteristic P ◽  
Motivic Cohomology ◽  
Cohomological Invariants ◽  
Group Schemes ◽  
Characteristic 2 ◽  
Theory Of Fields ◽  
Mod P

Abstract We determine the mod $p$ cohomological invariants for several affine group schemes $G$ in characteristic $p$. These are invariants of $G$-torsors with values in étale motivic cohomology, or equivalently in Kato’s version of Galois cohomology based on differential forms. In particular, we find the mod 2 cohomological invariants for the symmetric groups and the orthogonal groups in characteristic 2, which Serre computed in characteristic not 2. We also determine all operations on the mod $p$ étale motivic cohomology of fields, extending Vial’s computation of the operations on the mod $p$ Milnor K-theory of fields.

STRATIFYING SYSTEMS, FILTRATION MULTIPLICITIES AND SYMMETRIC GROUPS

2005 ◽  
Vol 04 (05) ◽  
pp. 551-555 ◽  
Author(s):  
KARIN ERDMANN
Keyword(s):  
Hecke Algebras ◽  
Symmetric Groups ◽  
Schur Algebras

We show that the theorem by Hemmer and Nakano, on uniqueness of Specht filtration multiplicities, can be proved working entirely with representations of symmetric groups, or Hecke algebras. Furthermore, we give a new proof that Schur algebras are quasi-hereditary provided the characteristic of the field is at least 5. Our tools are some more general results on stratifying systems.

scholarly journals Path combinatorics and light leaves for quiver Hecke algebras

2021 ◽  
Author(s):  
Chris Bowman ◽  
Anton Cox ◽  
Amit Hazi ◽  
Dimitris Michailidis
Keyword(s):  
Structural Information ◽  
Hecke Algebras ◽  
Symmetric Groups ◽  
Hecke Algebra ◽  
Classical Notion ◽  
Geometric Setting ◽  
Quiver Hecke Algebra

AbstractWe recast the classical notion of “standard tableaux" in an alcove-geometric setting and extend these classical ideas to all “reduced paths" in our geometry. This broader path-perspective is essential for implementing the higher categorical ideas of Elias–Williamson in the setting of quiver Hecke algebras. Our first main result is the construction of light leaves bases of quiver Hecke algebras. These bases are richer and encode more structural information than their classical counterparts, even in the case of the symmetric groups. Our second main result provides path-theoretic generators for the “Bott–Samelson truncation" of the quiver Hecke algebra.

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