相关论文: Cellularity of cyclotomic Yokonuma-Hecke algebras

We study the representation theory of the type B Schur algebra $\mathcal{L}^n(m)$ with unequal parameters introduced in work of Lai, Nakano and Xiang. For generic values of $q,Q$, this algebra is semi-simple and Morita equivalent to the…

We introduce the notion of a complex cell, a complexification of the cells/cylinders used in real tame geometry. For $\delta\in(0,1)$ and a complex cell $\mathcal{C}$ we define its holomorphic extension…

In this paper we give a symbolical formula and a cancellation-free formula for the Schur elements associated to the simple modules of the degenerate cyclotomic Hecke algebras. As some direct applications, we show that the Schur elements are…

In this article, we define and study the affine and cyclotomic Yokonuma-Hecke algebras. These algebras generalise at the same time the Ariki-Koike and affine Hecke algebras and the Yokonuma-Hecke algebras. We study the representation theory…

Given a quiver automorphism with nice properties, we give a presentation of the fixed subalgebra of the associated cyclotomic quiver Hecke algebra. Generalising an isomorphism of Brundan and Kleshchev between the cyclotomic Hecke algebra of…

In this paper, we define a quotient of the cyclotomic Hecke algebra of type $G(r,1,n)$ as a generalisation of the Temperley-Lieb algebras of type $A$ and $B$. We establish a graded cellular structure for the generalised Temperley-Lieb…

Inspired by the work [Ra1], we directly give a complete classification of irreducible calibrated representations of affine Yokonuma-Hecke algebras $\widehat{Y}_{r,n}(q)$ over $\mathbb{C},$ which are indexed by $r$-tuples of placed skew…

We provide an affine cellular structure on the extended affine Hecke algebra and affine $q$-Schur algebra of type $A_{n-1}$ that is defined over $\mathbb{Z}\left[q^{\pm1}\right]$, that is, without an adjoined $q^{\frac{1}{2}}$. This is with…

A cellular algebra is called cyclic cellular if all cell modules are cyclic. Most important examples of cellular algebras appearing in representation theory are in fact cyclic cellular. We prove that if $A$ is a cyclic cellular algebra,…

In this paper, and a second part to follow, we complete the programme (initiated more than 15 years ago) of determining the decomposition numbers and verifying James' Conjecture for Iwahori--Hecke algebras of exceptional type. The new…

We exhibit for all positive integers r, an explicit cellular structure for the endomorphism algebra of the r'th tensor power of an integral form of the Weyl module with highest weight d of the quantised enveloping algebra of sl2. When q is…

Weighted KLRW algebras are diagram algebras generalizing KLR algebras. This paper undertakes a systematic study of these algebras culminating in the construction of homogeneous affine cellular bases in affine types A and C, which…

A complete system of primitive pairwise orthogonal idempotents for cyclotomic Hecke algebras is constructed by consecutive evaluations of a rational function in several variables on quantum contents of multi-tableaux. This function is a…

We prove a Morita reduction theorem for the cyclotomic Hecke algebras H_{r,p,n}({q,Q})$ of type G(r,p,n). As a consequence, we show that computing the decomposition numbers of H_{r,p,n}(Q) reduces to computing the p'-splittable…

Just as the Temperley-Lieb algebra is a good place to compute the Jones polynomial, the Kauffman bracket skein algebra of a disk with $2k$ colored points on the boundary, each with color $n$, is a good place to compute the $n^{th}$ colored…

In this paper, we construct some integral bases for the cocenter of the cyclotomic Hecke algebra $\mathscr{H}_{n,K}$ of type $G(r,1,n)$ by generalizing Geck and Pfeiffer's work on the cocenters of the Iwahori-Hecke algebras associated to…

The paper studies the modular representation theory of the cyclotomic Hecke algebras of type $G(r,p,n)$ with $(\eps,q)$-separated parameters. We show that the decomposition numbers of these algebras are completely determined by the…

We first present an Iwahori-Matsumoto presentation of affine Yokonuma-Hecke algebras $\widehat{Y}_{r,n}(q)$ to give a new proof of the fact, which was previously proved by Chlouveraki and S\'echerre, that $\widehat{Y}_{r,n}(q)$ is a…

Let $S$ be the cyclotomic $q$-Schur algebra associated to the Ariki-Koike algebra $H_{n,r}$ of rank $n$, introduced by Dipper-James-Mathas. For each $p = (r_1, ..., r_g)$ such that $r_1 + ... + r_g = r$, we define a subalgebra $S^p$ of $S$…

We give two different approaches to classifying the simple modules of $0$-Yokonuma-Hecke algebras $Y_{r,n}(0)$ over an algebraically closed field of characteristic $p$ such that $p$ does not divide $r.$ Using the isomorphism between the…