Related papers: The Whittaker functional is a shifted microstalk

We study various categories of Whittaker modules over the queer Lie superalgebras $\mathfrak q(n)$. We formulate standard Whittaker modules and reduce the problem of composition factors of these standard Whittaker modules to that of Verma…

We consider a global, nonlinear version of the Whitney extension problem for manifold-valued smooth functions on closed domains $C$, with non-smooth boundary, in possibly non-compact manifolds. Assuming $C$ is a submanifold with corners, or…

In this paper we construct weighted path models to compute Whittaker vectors in the completion of Verma modules, as well as Whittaker functions of fundamental type, for all finite-dimensional simple Lie algebras, affine Lie algebras, and…

Let $F$ be either $\mathbb{R}$ or a finite extension of $\mathbb{Q}_p$, and let $G$ be a finite central extension of the group of $F$-points of a reductive group defined over $F$. Also let $\pi$ be a smooth representation of $G$ (Frechet of…

The goal of this paper is to study the structure of noncommutative weighted shifts, their properties, and to understand their role as models (up to similarity) for $n$-tuples of operators on Hilbert spaces as well as their implications to…

In previous work we have shown that the (\theta->\infty)-limit of \phi^4_4-quantum field theory on noncommutative Moyal space is an exactly solvable matrix model. In this paper we translate these results to position space. We show that the…

We study the behavior of slope-stability of reflexive twisted sheaves over a normal projective variety $X$ under pullback along a cover. Slope-stability is always preserved if the cover does not factor via a quasi-\'etale cover. Fixing the…

Here we construct spaces of coinvariants for Heisenberg vertex algebras on abelian varieties and show that these globalize to twisted $\mathscr{D}$-modules on the moduli space of abelian varieties. Remarkably, we recover the standard…

Let V be a vertex operator algebra, and for k a positive integer, let g be a k-cycle permutation of the vertex operator algebra V^{\otimes k}. We prove that the categories of weak, weak admissible and ordinary g-twisted modules for the…

Let $M(1)$ be the vertex operator algebra with the Virasoro element $\omega$ associated to the Heisenberg algebra of rank $1$ and let $M(1)^{+}$ be the subalgebra of $M(1)$ consisting of the fixed points of an automorphism of $M(1)$ of…

For a system of correlated electrons, the Luttinger-Ward functional provides a link between static thermodynamic quantities on the one hand and single-particle excitations on the other. The functional is useful to derive several general…

We define and study the subspace of cuspidal functions for $G$-bundles on a class of nilpotent extensions $C$ of curves over a finite field. We show that this subspace is preserved by the action of a certain noncommutative Hecke algebra…

Let $G=GL_{n}(F)$ and let $(\pi_{St},V)$ be a (generalized) Steinberg representation of $G$. It is well known that the space of Iwahori fixed vectors in $V$ is one dimensional. The Iwahori Hecke algebra acts on this space via a character.…

In this paper, Whittaker modules for the Schr\"odinger-Virasoro algebra $\mathfrak{sv}$ are defined. The Whittaker vectors and the irreducibility of the Whittaker modules are studied. $\mathfrak{sv}$ has a triangular decomposition according…

Let ${\mathfrak{g}}$ be a complex semisimple Lie algebra with Borel subalgebra ${\mathfrak{b}}$ and corresponding nilradical ${\mathfrak{n}}$. We show that singular Whittaker modules $M$ are simple if and only if the space $\hbox{Wh}\,M$ of…

We construct a conic Lagrangian in the cotangent bundle of the moduli stack of $G$-bundles over the universal curve, restricting to the global nilpotent cone for each curve. It gives rise to a singular support condition suitable for the…

We establish that Hitchin's connection exist for any rigid holomorphic family of Kahler structures on any compact pre-quantizable symplectic manifold which satisfies certain simple topological constraints. Using Toeplitz operators we prove…

We construct a weak categorification of the quantum toroidal algebra action on the Grothendieck group of moduli space of stable (or framed) sheaves over an algebraic surface, which is constructed by Schiffmann-Vasserot and Negu\c{t}. The…

We recall various multiple integrals related to the isotropic square Ising model, and corresponding, respectively, to the n-particle contributions of the magnetic susceptibility, to the (lattice) form factors, to the two-point correlation…

We construct a flat holomorphic line bundle over a connected component of the Hurwitz space of branched coverings of the Riemann sphere. A flat holomorphic connection defining the bundle is described in terms of the invariant Wirtinger…