Related papers: Some Hecke Algebra Products and Corresponding Rand…

We estimate the asymptotic growth of reciprocal conjugacy classes in Hecke groups using their free product structure and word lengths of reciprocal elements. Our approach is different from other works in this direction and uses tools from…

We give a new construction of primitive idempotents of the Hecke algebras associated with the symmetric groups. The idempotents are found as evaluated products of certain rational functions thus providing a new version of the fusion…

Random walks in random scenery are processes defined by $Z_n:=\sum_{k=1}^n\xi_{X_1+...+X_k}$, where $(X_k,k\ge 1)$ and $(\xi_y,y\in\mathbb Z)$ are two independent sequences of i.i.d. random variables. We suppose that the distributions of…

Let $H(\lambda_4)$ be the Hecke group $\langle x,y\,:\, x^2=y^4=1 \rangle$ and, for a square-free positive integer $n$, consider the subset $\mathbb{Q}^*(\sqrt{-n})=\left\{(a+\sqrt{-n})/c \, | \, a,b=(a^2+n)/c \in \mathbb{Z},\, c\in…

We analyze Hecke pairs (G,H) and the associated Hecke algebra when G is a semidirect product N x Q and H = M x R for subgroups M of N and R of Q with M normal in N. Conditions are given in terms of N, Q, M, and R which are equivalent to the…

Hecke symmetries generalize the usual tensor symmetry of vector spaces $v\otimes w\arrow w\otimes v$ as well as the symmetry of vector superspaces. To a Hecke symmetry $R$ there associates a quadratic algebra which can be interpreted as the…

The traces of the Murphy operators of the Hecke algebra $H_n(q)$, and of products of sets of Murphy operators with non-consecutive indices, can be evaluated by a straightforward recursive procedure. These traces are shown to determine all…

Algebraic random walks (ARW) and quantum mechanical random walks (QRW) are investigated and related. Based on minimal data provided by the underlying bialgebras of functions defined on e. g the real line R, the abelian finite group Z_N, and…

In this article we classify all infinitesimal Hecke algebras of so_N. We establish isomorphism of their universal versions and the W-algebras of so_{N+2m+1} with a 1-block nilpotent element of the Jordan type (1,...,1,2m+1). This should be…

We generalize Reiner--Saliola--Welker's well-known but mysterious family of *$k$-random-to-random shuffles* from Markov chains on symmetric groups to Markov chains on the Type-$A$ Iwahori--Hecke algebras. We prove that the family of…

Let $G$ be a finite group, $H \le G$ a subgroup, $R$ a commutative ring, $A$ an $R$-algebra, and $\alpha$ an action of $G$ on $A$ by $R$-algebra automorphisms. We study the associated \emph{skew Hecke algebra}…

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…

In this paper, we investigate a connection between convolution products for quiver Hecke algebras and tensor products for quantum groups. We give a categorification of the natural projection $ \pi_{\lambda, \mu} :…

We study a family of shuffling operators on the symmetric group $S_n$, which includes the top-to-random shuffle. The general shuffling scheme consists of removing one card at a time from the deck (according to some probability distribution)…

For any Hecke symmetry $R$ there is a natural quantization $A_n(R)$ of the Weyl algebra $A_n$. The aim of this paper is to study some general ring-theoretic aspects of $A_n(R)$ and its relations to formal deformations of $A_n$. We also…

We study Hecke algebras of groups acting on trees with respect to geometrically defined subgroups. In particular, we consider Hecke algebras of groups of automorphisms of locally finite trees with respect to vertex and edge stabilizers and…

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…

The involution walk is the random walk on $S_n$ generated by involutions with a binomially distributed with parameter $1-p$ number of $2$-cycles. This is a parallelization of the transposition walk. The involution walk is shown in this…

We consider a family of Hecke C*-algebras which can be realised as crossed products by semigroups of endomorphisms. We show by dilating representations of the semigroup crossed product that the category of representations of the Hecke…

We study the ideal theory of amalgamated products of Ore and quadratic extensions over a base ring R. We prove an analogue of the Hilbert Basis theorem for an amalgamated product Q of quadratic extensions and determine conditions for when…