相关论文: Cellularity of cyclotomic Yokonuma-Hecke algebras

We recall Lusztig's construction of the asymptotic Hecke algebra $J$ of a Coxeter system $(W,S)$ via the Kazhdan--Lusztig basis of the corresponding Hecke algebra. The algebra $J$ has a direct summand $J_E$ for each two-sided…

We show how to use Jantzen's sum formula for Weyl modules to prove semisimplicity criteria for endomorphism algebras of $\textbf{U}_q$-tilting modules (for any field $\mathbb{K}$ and any parameter $q\in\mathbb{K}-\{0,-1\}$). As an…

This paper develops an abstract framework for constructing ``seminormal forms'' for cellular algebras. That is, given a cellular R-algebra A which is equipped with a family of JM-elements we give a general technique for constructing…

We introduce the notion of modular $q$-holonomic modules whose fundamental matrices define a cocycle with improved analyticity properties and show that the generalised $q$-hypergeometric equation, as well as three key $q$-holonomic modules…

Over an arbitrary commutative ring $R$, we develop a theory of quantum cellular automata. We then use algebraic K-theory to construct a space $\mathbf{Q}(X)$ of quantum cellular automata (QCA) on a given metric space $X$. In most cases of…

This chapter is based on a series of lectures that I gave at the National University of Singapore in April 2013. The notes survey the representation theory of the cyclotomic Hecke algebras of type A with an emphasis on understanding the KLR…

Inspired by the work [PA1], in this note, we prove that a complete set of pairwise orthogonal primitive idempotents of Yokonuma-Hecke algebras can be obtained by consecutive evaluations of a certain rational function.

We prove two results intended to streamline proofs about cellularity that pass through mutual algebraicity. First, we show that a countable structure $M$ is cellular if and only if $M$ is $\omega$-categorical and mutually algebraic. Second,…

Let $ \mathbb{A}$ be a cellular algebra over a field $\mathbb{F}$ with a decomposition of the identity $ 1_{\mathbb{A}} $ into orthogonal idempotents $ e_i$, $i \in I$ (for some finite set $I$) satisfying some properties. We describe the…

In this article, we give an explicit construction of the simple modules for both non-degenerate and degenerate cyclotomic Hecke-Clifford superalgebras over an algebraically closed field of characteristic not equal to $2$ under certain…

By a result of Mathas, the basis element T_{w_0} of the Hecke algebra of a finite Coxeter group acts in the canonical basis of a cell module as a permutation matrix times plus or minus a power of v. We generalize this result to the unequal…

We use a skein-theoretic version of the Hecke algebras of type A to present three-dimensional diagrammatic views of Gyoja's idempotent elements, based closely on the corresponding Young diagram. In this context we give straightforward…

We give a simple construction of Markov traces for Iwahori-Hecke algebras associated with infinite series of crystallographic Coxeter groups. In types B and D it is new, and generalizes a known construction in type A employing symmetric…

We study the cocenter of the cyclotomic quiver Hecke algebra $R^\Lambda_\alpha$ associated to an {\it arbitrary} symmetrizable Cartan matrix $A=(a_{ij})_{i,j}\in I$, $\Lambda\in P^+$ and $\alpha\in Q_n^+$. We introduce a notion called…

Let $R$ be a commutative ring with identity and let $V$ be a free $R$-module of rank $n$ for some $n\in\mathbb{N}$. Fixing an $R$-basis $\mathcal{E}$ of $V$, the symmetric group $\mathfrak{S}_n$ acts on $V$ by permuting $\mathcal{E}$ and…

We relate the classes of unitary and calibrated representations of cyclotomic Hecke algebras and, in particular, we show that for the most important deformation parameters these two classes coincide. We classify these representations in…

Let H(R,q) be an affine Hecke algebra with a positive parameter function q. We are interested in the topological K-theory of H(R,q), that is, the K-theory of its C*-completion C*_r (R,q). We will prove that $K_* (C*_r (R,q))$ does not…

We compute the centre of the cyclotomic Hecke algebra attached to $G(m,1,2)$ and show that if $q \neq 1$ it is equal to the image of the centre of the affine Hecke algebra $\Ha$. We also briefly discuss what is known about the relation…

We construct a cellular basis of the walled Brauer algebra which has similar properties as the Murphy basis of the group algebra of the symmetric group. In particular, the restriction of a cell module to a certain subalgebra can be easily…

We present a development of cellular cohomology in homotopy type theory. Cohomology associates to each space a sequence of abelian groups capturing part of its structure, and has the advantage over homotopy groups in that these abelian…