Related papers: Structure coefficients for Jack characters: approx…
We enumerate factorizations of a Coxeter element in a well generated complex reflection group into arbitrary factors, keeping track of the fixed space dimension of each factor. In the infinite families of generalized permutations, our…
With reference to a baseline parametrization, we explore highly efficient fractional factorial designs for inference on the main effects and, perhaps, some interactions. Our tools include approximate theory together with certain carefully…
The graph of zigzag diagrams is a close relative of Young's lattice. The boundary problem for this graph amounts to describing coherent random permutations with descent-set statistic, and is also related to certain positive characters on…
We use the Jack symmetric functions as a basis of the Fock space, and study the action of the Virasoro generators $L_n$. We calculate explicitly the matrix elements of $L_n$ with respect to the Jack-basis. A combinatorial procedure which…
Superpolynomials consist of commuting and anti-commuting variables. By considering the anti-commuting variables as a module of the symmetric group the theory of vector-valued nonsymmetric Jack polynomials can be specialized to…
We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another…
We investigate linear combinations of characters for minimal Virasoro models which are representable as a products of several basic blocks. Our analysis is based on consideration of asymptotic behaviour of the characters in the…
We introduce a class of $f(t)$-factorials, or $f(t)$-Pochhammer symbols, that includes many, if not most, well-known factorial and multiple factorial function variants as special cases. We consider the combinatorial properties of the…
The combination of the group ring setting with the methods of character theory allows an elegant and powerful analysis of various combinatorial structures, via their character sums. These combinatorial structures include difference sets,…
The monomial basis for polynomials in N variables is labeled by compositions. To each composition there is associated a hook-length product, which is a product of linear functions of a parameter. The zeroes of this product are related to…
In a recent paper, the authors introduced a new basis of the ring of symmetric functions which evaluate to the irreducible characters of the symmetric group at roots of unity. The structure coefficients for this new basis are the stable…
A fast approximation to the Boys functions (related to the lower incomplete gamma function of half-integer parameter) by a single closed-form analytical expression for all argument values have been developed and tested. Besides the…
We define character varieties with non-connected structure groups of finitely presented discrete groups and study some basic aspects, such as generic conjugacy classes and relation with fixed points in character varieties with connected…
We extend the classical construction of operator colligations and characteristic functions. Consider the group $G$ of finite block unitary matrices of size $\alpha+\infty+...+\infty$ ($k$ times). Consider the subgroup $K=U(\infty)$, which…
We give an $AB$-factorization of the supercharacter table of the group of $n\times n$ unipotent upper triangular matrices over $\FF_q$, where $A$ is a lower-triangular matrix with entries in $\ZZ[q]$ and $B$ is a unipotent upper-triangular…
Lusztig conjectured that the almost characters of a finite reductive group are up to a scalar the same as the characteristic functions of the rational character sheaves defined on the corresponding algebraic group. We propose in this paper…
Stanley symmetric functions are the stable limits of Schubert polynomials. In this paper, we show that, conversely, Schubert polynomials are Demazure truncations of Stanley symmetric functions. This parallels the relationship between Schur…
In this series of papers, we study correspondence between the following: (1) large scale structure of the metric space bigsqcup_m {Cay(G(m))} consisting of Cayley graphs of finite groups with k generators; (2) structure of groups which…
Motivated by statistical applications, this paper introduces Cauchy identities for characters of the compact classical groups. These identities generalize the well-known Cauchy identity for characters of the unitary group, which are Schur…
We study the normal approximation of functionals of Poisson measures having the form of a finite sum of multiple integrals. When the integrands are nonnegative, our results yield necessary and sufficient conditions for central limit…