Related papers: Equating decomposition numbers for different prime…
Let H = H (R,q) be an affine Hecke algebra with complex, possibly unequal parameters q, which are not roots of unity. We compute the Hochschild and the cyclic homology of H. It turns out that these are independent of q and that they admit…
Inspired by the work of Rostam, we establish an explicit categorical equivalence between affine Yokonuma-Hecke algebras and quiver Hecke algebras associated to disjoint copies of quivers of (affine) type $A,$ generalizing Rouquier's…
Primes in the two complete associative normed division algebras C and H have affinities with structures seen in the standard model of particle physics. On the integers in the two algebras, there are two equivalence relations: a strong one,…
We compare two generalisations of the notion of hook lengths for partitions. We apply this in the context of the modular representation theory of Ariki-Koike algebras. We show that the Schur element of a simple module is divisible by the…
We define the formal affine Demazure algebra and formal affine Hecke algebra associated to a Kac-Moody root system. We prove the structure theorems of these algebras, hence, extending several result and construction (presentation in terms…
Recently a new technique in the harmonic analysis on symmetric spaces was suggested based on certain remarkable representations of affine and double affine Hecke algebras in terms of Dunkl and Demazure operators instead of Lie groups and…
We will classify finite dimensional irreducible modules for affine quantum Schur algebras at roots of unity and generalize \cite[(6.5f) and (6.5g)]{Gr80} to the affine case in this paper.
In this paper the authors investigate the $q$-Schur algebras of type B that were constructed earlier using coideal subalgebras for the quantum group of type A. The authors present a coordinate algebra type construction that allows us to…
Under the assumption that the quantum parameter $q$ is an $l$-th primitive root of unity with $l$ odd in a field $F$ of characteristic 0 and $m+n\geq r$, we obtained a complete classification of irreducible modules of the $q$-Schur…
We investigate the structure of the Hecke algebras related to the unimodular and modular group over hermitian fields and definite quaternion algebras. In particular we show that in general there is no decomposition into primary components.…
We classify gradings on the Hecke category that refine the standard integer grading. We also classify object-preserving autoequivalences of the Hecke category. We obtain a natural bigrading on the Hecke category which is related to the…
We study the Hecke algebra $\H(\bq)$ over an arbitrary field $\FF$ of a Coxeter system $(W,S)$ with independent parameters $\bq=(q_s\in\FF:s\in S)$ for all generators. This algebra is always linearly spanned by elements indexed by the…
Recently Tewari and van Willigenburg constructed modules of the 0-Hecke algebra that are mapped to the quasisymmetric Schur functions by the quasisymmetric characteristic and decomposed them into a direct sum of certain submodules. We show…
The main result of this paper shows that, over large enough fields of characteristic different from $2$, the alternating Hecke algebras are $\mathbb{Z}$-graded algebras that are isomorphic to fixed-point subalgebras of the quiver Hecke…
This paper deals with quon algebras or deformed oscillator algebras, for which the deformation parameter is a root of unity. We show the interest of such algebras for fractional supersymmetric quantum mechanics, angular momentum theory and…
We construct modules of the $0$-Hecke algebra whose images under the quasisymmetric characteristic map are the Young row-strict quasisymmetric Schur functions. This provides a representation-theoretic interpretation of this basis of…
This paper reviews a result of Jensen on characters of some tilting modules for $\SL_3(k)$, where $k$ has characteristic at least five and fills in some gaps in the proof of this result. We then apply the result to finding some…
We deduce the Schaper formula for Hecke-algebras at root of unity from the Jantzen conjecture in the LLT-setup. This explains an observation due to R. Rouquier.
We prove a $q$-analogue of the Carter-Payne theorem for the two special cases corresponding to moving an arbitrary number of nodes between adjacent rows, or moving one node between an arbitrary number of rows. As a consequence, we show that…
Let ${\mathcal H}_{q}(d)$ be the Iwahori-Hecke algebra for the symmetric group, where $q$ is a primitive $l$th root of unity. In this paper we develop a theory of support varieties which detects natural homological properties such as the…