Related papers: Structure coefficients for Jack characters: approx…

We study the real spectrum compactification of character varieties of finitely generated groups in semisimple Lie groups. This provides a compactification with good topological properties, and we interpret the boundary points in terms of…

In this paper, we study connections between the structure of a group and the structure of the group (under pointwise product) of its polynomial functions.

In the principles-and-parameters framework, the structural features of languages depend on parameters that may be toggled on or off, with a single parameter often dictating the status of multiple features. The implied covariance between…

We study the intermediate extension of the character sheaves on an adjoint group to the semi-stable locus of its wonderful compactification. We show that the intermediate extension can be described by a direct image construction. As a…

We study correlation functions of the characteristic polynomials in coupled matrix models based on the Schur polynomial expansion, which manifests their determinantal structure.

In this paper, we derive a relation of new kind between certain character values of symmetric groups in terms of so-called maya diagrams. We also investigate a relation between our result and Bernstein's creation operators for Schur…

This is a survey of some recent developments in the study of complements of line arrangements in the complex plane. We investigate the fundamental groups and finite covers of those complements, focusing on homological and enumerative…

Let (G,K) be a symmetric pair over the complex numbers, and let X=K\G be the corresponding symmetric space. In this paper we study a nearby cycles functor associated to a degeneration of X to MN\G, which we call the "wonderful…

We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position…

In math.CO/0109093 the author obtained a formula for the value of an irreducible symmetric group character indexed by a partition of rectangular shape. In the present paper this formula is (conjecturally) generalized to arbitrary shapes.

We explore the notion of sectional number of a group homomorphism, leading to a generalization of the covering number of a group, and present several characterizations when the sectional number is finite, providing estimates for computing…

In this short note we study uniform approximations to the normal distributions by Jacobi theta functions. We shall show that scaled theta functions approach to a normal distribution exponentially fast.

Stanley considered suitably normalized characters of the symmetric groups on Young diagrams having a special geometric form, namely multirectangular Young diagrams. He proved that the character is a polynomial in the lengths of the sides of…

Using the wonderful compactification of a semisimple adjoint affine algebraic group G defined over an algebraically closed field k of arbitrary characteristic, we construct a natural compactification Y of the G-character variety of any…

Noting a curious link between Andrews' even-odd crank and the Stanley rank, we adopt a combinatorial approach building on the map of conjugation and continue the study of integer partitions with parts separated by parity. Our motivation is…

A new generalization of the Jack polynomials that incorporates fermionic variables is presented. These Jack superpolynomials are constructed as those eigenfunctions of the supersymmetric extension of the trigonometric…

The expectation of the descent number of a random Young tableau of a fixed shape is given, and concentration around the mean is shown. This result is generalized to the major index and to other descent functions. The proof combines…

We construct a new family of homomorphisms from Specht modules into Foulkes modules for the symmetric group. These homomorphisms are used to give a combinatorial description of the minimal partitions (in the dominance order) which label…

We introduce a generalization of immanants of matrices, using partition algebra characters in place of symmetric group characters. We prove that our immanant-like function on square matrices, which we refer to as the recombinant, agrees…

In this study, we derive the density and distribution function of a ratio of the largest and smallest eigenvalues of a singular beta-Wishart matrix for the sphericity test. These functions can be expressed in terms of the product of Jack…