Related papers: Graded characters, demazure multiplicities, and ch…
By enforcing invariance under S-duality in type IIB string theory compactified on a Calabi-Yau threefold, we derive modular properties of the generating function of BPS degeneracies of D4-D2-D0 black holes in type IIA string theory…
Graded Hecke algebras can be constructed in terms of equivariant cohomology and constructible sheaves on nilpotent cones. In earlier work, their standard modules and their irreducible modules where realized with such geometric methods. We…
We describe a categorification of the Double Affine Hecke Algebra (${\mathcal{H}\kern -.4em\mathcal{H}}$) associated with an affine Lie algebra $\widehat{\mathfrak{g}}$, including a categorification of the polynomial representation and…
The Nekrasov partition function in supersymmetric quantum gauge theory is mathematically formulated as an equivariant integral over certain moduli spaces of sheaves on a complex surface. In ``Seiberg-Witten Theory and Random Partitions'',…
We find continuous families of supersymmetric flux vacua in IIB Calabi-Yau compactifications for multiparameter manifolds with an appropriate $\mathbb{Z}_2$ symmetry. We argue, supported by extensive computational evidence, that the…
Let $ \Bbb V = \coprod_{h = 0}^{\infty} \Bbb V_h$ be the graded monster module of the monster simple group $\Bbb M$ and let $\chi_k$ be an irreducible representation of $\Bbb M$. The generating function of $c_{hk}$ (the multiplicity of…
We survey recent progress in the study of moduli of vector bundles on higher-dimensional base manifolds. In particular, we discuss an algebro-geometric construction of an analogue for the Donaldson-Uhlenbeck compactification and explain how…
We provide identities of inverse Chevalley type for the graded characters of level-zero Demazure submodules of extremal weight modules over a quantum affine algebra of type $C$. These identities express the product $e^{\mu} \, \mathrm{gch}…
A Lefschetz module is a module over a graded algebra $A$ that satisfies analogues of Poincar\'{e} duality, the Hard Lefschetz property, and the Hodge--Riemann relations with respect to an open convex cone $\mathscr{K}$ in the degree one…
Recently, degenerate Cauchy numbers and polynomials are introduced in [10]. In this paper, we study the degenerate Cauchy numbers and polynomials which are different from the previous degenerate Cauchy numbers and polynomials. In addition,…
A classic result of Ritt describes polynomials invertible in radicals: they are compositions of power polynomials, Chebyshev polynomials and polynomials of degree at most 4. In this paper we prove that a polynomial invertible in radicals…
The generalized Kostka polynomials are the Poincare polynomials of isotypic components of certain graded GL(n)-modules. The former satisfy a monotonicity property arising from natural surjections of the corresponding modules. This…
Over a subfield of the field of complex numbers, the Hodge realization of a geometrical motive is defined and represented as the cohomology of a mixed Hodge DG-complex in the sense of Deligne. Both filtrations are represented by truncation…
We define and study the Kirillov--Reshetikhin modules for algebras of type $G_2$. We compute the graded character of these modules and verify that they are in accordance with the conjectures in math.QA/981202 and math.QA/0102113. These…
We study the classical limit of a family of irreducible representations of the quantum affine algebra associated to $\mathfrak{sl}_{n+1}$. After a suitable twist, the limit is a module for $\mathfrak{sl}_{n+1}[t]$, i.e., for the maximal…
In this paper we introduce Besov-Morrey spaces with all indices variable and study some fundamental properties. This includes a description in terms of Peetre maximal functions and atomic and molecular decompositions. This new scale of…
We characterize subsets of highest weight $\mathfrak{g}$-crystals that arise as unions of Demazure crystals, for any symmetrizable Kac-Moody Lie algebra $\mathfrak{g}$. We provide a local characterization for these subsets and prove they…
To every $h + \mathbb{N}$-graded module $M$ over an $\mathbb{N}$-graded conformal vertex algebra $V$, we associate an increasing filtration $(G^pM)_{p \in \mathbb{Z}}$ which is compatible with the filtrations introduced by Haisheng Li. The…
We study a class of modules, called Chari-Venkatesh modules, for the current superalgebra $\mathfrak{sl}(1|2)[t]$. This class contains other important modules, such as graded local Weyl, truncated local Weyl and Demazure-type modules. We…
Let $\mathfrak{g}$ be a semisimple Lie algebra over $\mathbb{C}$ having rank $l$ and let $V=L(\lambda)$ be an irreducible finite-dimensional $\mathfrak{g}$-module having highest weight $\lambda.$ Computations of weight multiplicities in…