Related papers: Generalized Markov traces and Jucys-Murphy element…

Using an intrinsic $q$-hypergeometric strategy, we generalise Dwork-type congruences $H(p^{s+1})/H(p^s)\equiv H(p^s)/H(p^{s-1})\pmod{p^3}$ for $s=1,2,\dots$ and $p$ a prime, when $H(N)$ are truncated hypergeometric sums corresponding to the…

This paper is a continuation of a previous paper in which the first two authors have introduced the spherical Hecke algebra and the Satake isomorphism for an untwisted affine Kac-Moody group over a non-archimedian local field. In this paper…

The class of normal subshifts includes irreducible infinite topological Markov shifts, irreducible infinite sofic shifts, synchronized systems, Dyck shifts, $\beta$-shifts, substitution minimal shifts, and so on. We will characterize…

We construct simple geometric operations on faces of the Cayley sum of two polytopes. These operations can be thought of as convex geometric counterparts of divided difference operators in Schubert calculus. We show that these operations…

We study non-linear traces of Choquet type and Sugeno type on matrix algebras. They have certain partial additivities. We show that these partial additivities characterize non-linear traces of both Choquet type and Sugeno type respectively.…

Standard results from non-abelian cohomology theory specialize to a theory of torsors and stacks for cosimplicial groupoids. The space of global sections of the stack completion of a cosimplicial groupoid $G$ is weakly equivalent to the…

We study generalized Jacobi sums, cyclotomic numbers, and $d$-compositions in Thaine's framework, and prove new multiplicative identities extending Davenport and Hasse's lifting theorem from the classical prime-power setting to products of…

The goal of the present paper is to provide a detailed study of irreducible representations of the algebra generated by the symmetries of the generic quantum superintegrable system on the $d$-sphere. Appropriately normalized, the symmetry…

We generalize Lusztig's nilpotent varieties, and Kashiwara and Saito's geometric construction of crystal graphs from the symmetric to the symmetrizable case. We also construct semicanonical functions in the convolution algebras of…

Motivated by work of Coxeter (1957), we study a class of algebras associated to Coxeter groups, which we term 'generalized nil-Coxeter algebras'. We construct the first finite-dimensional examples other than usual nil-Coxeter algebras;…

Let $A$ be a not necessarily commutative monoid with zero such that projective $A$-acts are free. This paper shows that the algebraic K-groups of $A$ can be defined using the +-construction and the Q-construction. It is shown that these two…

We study a commuting family of elements of the walled Brauer algebra $B_{r,s}(\delta)$, called the Jucys-Murphy elements, and show that the supersymmetric polynomials in these elements belong to the center of the walled Brauer algebra. When…

We investigate when a skew polynomial extension T = R[x; {\sigma}, {\delta}] of a Hopf algebra R admits a Hopf algebra structure, substantially generalising a theorem of Panov. When this construction is applied iteratively in characteristic…

We associate with every Renner monoid $R$ a \emph{generic Hecke algebra} $\H(R)$ over $\mathbb{Z}[q]$ which is a deformation of the monoid $\mathbb{Z}$-algebra of $R$. If $M$ is a finite reductive monoid with Borel subgroup $B$ and…

In this paper we study stable finiteness of ample groupoid algebras with applications to inverse semigroup algebras and Leavitt path algebras, recovering old results and proving some new ones. In addition, we develop a theory of (faithful)…

A characterization is given for directed graphs that yield graph $C^*$-algebras with continuous trace. This is established for row-finite graphs with no sources first using a groupoid approach, and extended to the general case via the…

We generalize random-to-random shuffling from a Markov chain on the symmetric group to one on the Type A Iwahori Hecke algebra, and show that its eigenvalues are polynomials in q with non-negative integer coefficients. Setting q=1 recovers…

We introduce Coxeter-sortable elements of a Coxeter group W. For finite W, we give bijective proofs that Coxeter-sortable elements are equinumerous with clusters and with noncrossing partitions. We characterize Coxeter-sortable elements in…

Using norms, the second author constructed a basis for the centre of the Hecke algebra of the symmetric group over $\Q[\xi]$ in 1990. An integral "minimal" basis was later given by the first author in 1999, following work of Geck and…

We generalize Kontsevich's construction of L-infinity derivations of polyvector fields from the affine space to an arbitrary smooth algebraic variety. More precisely, we construct a map (in the homotopy category) from Kontsevich's graph…