Related papers: Interpolating between promotion and the long cycle

We consider the distribution of the major index on standard tableaux of arbitrary straight shape and certain skew shapes. We use cumulants to classify all possible limit laws for any sequence of such shapes in terms of a simple auxiliary…

We study the properties of the multiplicative structure on valuations on convex sets. We prove a new version of the hard Lefschetz theorem for even translation invariant continuous valuations, and discuss related problems of integral…

We prove "untyping" theorems: in some typed theories (semirings, Kleene algebras, residuated lattices, involutive residuated lattices), typed equations can be derived from the underlying untyped equations. As a consequence, the…

Primary Cyclic matrices were used (but not named) by Holt and Rees in their version of Parker's MEAT-AXE algorithm to test irreducibility of finite matrix groups and algebras. They are matrices $X$ with at least one cyclic component in the…

This paper classifies and constructs explicitly all the irreducible representations of affine Hecke algebras of rank two root systems. The methods used to obtain this classification are primarily combinatorial and are, for the most part, an…

We identify a subalgebra \pH_n of the extended affine Hecke algebra \eH_n of type A. The subalgebra \pH_n is a \u-analogue of the monoid algebra of \S_n \ltimes \ZZ_{\geq 0}^n and inherits a canonical basis from that of \eH_n. We show that…

Let p be a prime number. We give a conjecture of a sheaf-theoretic nature which is equivalent to the strong form of the Tate conjecture for smooth, projective varieties X over F_p: for all n>0, the order of pole of the Hasse-Weil zeta…

With every family of finitely many subsets of a finite-dimensional vector space over the Galois-field with two elements we associate a cyclic transversal polytope. It turns out that those polytopes generalize several well-known polytopes…

Yannakakis' theorem relating the extension complexity of a polytope to the size of a nonnegative factorization of its slack matrix is a seminal result in the study of lifts of convex sets. Inspired by this result and the importance of lifts…

We give explicit isomorphisms between simple modules of degenerate cyclotomic Hecke algebras defined via various cellular bases. A special case gives a generalized Mullineux involution in the degenerate case.

We apply the classical technique on cyclic objects of Alain Connes to various objects, in particular to the higher Chow complex of S. Bloch to prove a Connes periodicity long exact sequence involving motivic cohomology groups. The Cyclic…

For a compact and convex window, Mecke described a process of tessellations which arise from cell divisions in discrete time. At each time step, one of the existing cells is selected according to an equally-likely law. Independently, a line…

In this paper we establish an order statistics model of Young tableaux. Multiple integration over nested simplexes is applied to the enumeration of Young tableaux. A brief proof of Frobenius-Young's and Aitken's formulas is given. Partially…

We present a certain generalization of a recent result of M. I. Cirnu on linear recurrence relations with coefficient in progressions [2]. We provide some interesting examples related to some well-known integer sequences, such as Fibonacci…

In the note some construction of Lie algebras is introduced. It is proved that the construction has the same property as a well known wreath product of groups [1]: Any extension of groups can be embedded into their wreath product [2].

We prove the existence of a sequence of commutative diagrams generalizing existing results on the cohomology of the Borel-Serre boundary and well-rounded retract to the context of the well-tempered complex. Our main theorem provides a…

This paper makes precise the close connection between the affine Hecke algebra, the path model, and the theory of crystals. Section 2 is a basic pictorial exposition of Weyl groups and affine Weyl groups and Section 5 is an exposition of…

The paper constructs new Hecke endomorphism algebras with a stratified structure. A novel feature of the proof is to approach difficult Ext^1 vanishing conditions by building entire exact category structures in which the analogous vanishing…

This paper investigates the connections between buildings and Hecke algebras through the combinatorial study of two algebras spanned by averaging operators on buildings. As a consequence we obtain a geometric and combinatorial description…

In this paper we give a combinatorial characterization of projections of geodesics in Euclidean buildings to Weyl chambers. We apply these results to the representation theory of complex semisimple Lie groups and to spherical Hecke rings…