Related papers: Weyl-Mahonian Statistics for Weighted Flags of Typ…
We continue to investigate the relation between the Mahler measure of certain two variable polynomials, the values of the Bloch--Wigner dilogarithm $D(z)$ and the values $\zeta_F(2)$ of zeta functions of number fields. Specifically, we…
We introduce a family of unital associative algebras A which are multiparameter analogues of the Weyl algebras and determine the simple weight modules and the Whittaker modules for them. All these modules can be regarded as spaces of…
In this paper, we characterize a duality relation between Eulerian recurrences and Eulerian recurrence systems, which generalizes and unifies Hermite-Biehler decompositions of several enumerative polynomials, including flag descent…
By the symmetric properties of Drichlet's type multiple q-l-function, we establish various identities concerning the generalized higher-order q-Euler polynomials. Furthermore, we give some interesting relationship between the power sums and…
We define the odd symplectic grassmannians and flag manifolds, which are smooth projective varieties equipped with an action of the odd symplectic group and generalizing the usual symplectic grassmannians and flag manifolds. Contrary to the…
Polynomials on stranded graphs are higher dimensional generalization of Tutte and Bollob\'as-Riordan polynomials [Math. Ann. 323 (2002), 81-96]. Here, we deepen the analysis of the polynomial invariant defined on rank 3 weakly-colored…
The `Weyl symmetric functions' studied here naturally generalize classical symmetric (polynomial) functions, and `Weyl bialternants,' sometimes also called Weyl characters, analogize the Schur functions. For this generalization, the…
We study the representation theory of the nested instantons quiver presented in [1], which describes a particular class of surface defects in four-dimensional supersymmetric gauge theories. We show that the moduli space of its stable…
We give an easy diagrammatical description of the parabolic Kazhdan-Lusztig polynomials for the Weyl group $W_n$ of type $D_n$ with parabolic subgroup of type $A_n$ and consequently an explicit counting formula for the dimension of the…
A new extension of the major index, defined in terms of Coxeter elements, is introduced. For the classical Weyl groups of type $B$, it is equidistributed with length. For more general wreath products it appears in an explicit formula for…
We study geometric and combinatorial properties of the degenerate flag varieties of type A. These varieties are acted upon by the automorphism group of a certain representation of a type A quiver, containing a maximal torus T. Using the…
A relationship between signed Eulerian polynomials and the classical Eulerian polynomials on $\mathfrak{S}_n$ was given by D\'{e}sarm\'{e}nien and Foata in 1992, and a refined version, called signed Euler-Mahonian identity, together with a…
In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.
For a general dyadic grid, we give a Calder\'{o}n-Zygmund type decomposition, which is the principle fact about the multilinear maximal function $\mathfrak{M}$ on the upper half-spaces. Using the decomposition, we study the boundedness of…
Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper we prove a family of identities involving Bernoulli numbers and apply them to obtain…
We obtain Hamel--Goulden-type ribbon decomposition determinantal formulas for flagged supersymmetric Schur functions. As an application, we derive corresponding new determinantal formulas dual refined canonical stable Grothendieck…
In algebraic geometry, one studies the solutions to polynomial equations, or, equivalently, to linear partial differential equations with constant coefficients. These lecture notes address the more general case when the coefficients are…
The charge is an intricate statistic on words, due to Lascoux and Schutzenberger, which gives positive combinatorial formulas for Lusztig's q-analogue of weight multiplicities and the energy function on affine crystals, both of type A. As…
We compute the automorphism groups of finite and cofinite ind-grassmannians, as well as of the ind-variety of maximal flags indexed by Z_{>0}. We pay special attention to differences with the case of ordinary flag varieties.
For classical groups SL(n), SO(n) and Sp(2n), we define uniformly geometric valuations on the corresponding complete flag varieties. The valuation in every type comes from a natural coordinate system on the open Schubert cell and is…