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The previous supersymmetric generalization of the unitary Harish--Chandra integral prompted the conjecture that the Harish--Chandra formula should extend to all classical supergroups. We prove this conjecture for the unitary orthosymplectic…
In this short note, we give a simple proof of a Lee-Yang type theorem which appeared in "Lee-Yang theorems and the complexity of computing averages" by Alistair Sinclair and Piyush Srivastava.
We prove the finiteness of the cohomology of torsion-free lattices in a semisimple Lie group of real rank one with coefficients in the distribution vector globalization of Harish-Chandra modules. The cohomology is expressed in terms of…
In this paper, we are concerned with studying the existence of invariant complex manifolds of two-dimensional holomorphic systems. From the geometric singular perturbation theory we know that if a slow-fast system has associated a normally…
We give a complete classification of all simple current modular invariants, extending previous results for $(\Zbf_p)^k$ to arbitrary centers. We obtain a simple explicit formula for the most general case. Using orbifold techniques to this…
Motivated by Harish-Chandra theory, we construct, starting from a simple CDD\--pole $S$\--matrix, a hierarchy of new $S$\--matrices involving ever ``higher'' (in the sense of Barnes) gamma functions.These new $S$\--matrices correspond to…
In this paper we give a discrete version of Hardy's uncertainty principle, by using complex variable arguments, as in the classical proof of Hardy's principle. Moreover, we give an interpretation of this principle in terms of decaying…
We give a new proof of Mikhalkin's Theorem on the topological classification of simple Harnack curves, which in particular extends Mikhalkin's result to real pseudoholomorphic curves.
In paper I of his masterpiece Harmonic Analysis on Real Reductive Groups, Harish-Chandra included an important inequality that is useful in proving that certain key integrals depending on a parameter converge for large values of the…
According to Chen and Fu's method, we offer a short proof for Dougall's $_2H_2$-series identity.
This paper is devoted to studying the centre of the multi-parameter quantum group $U_{q,G}(\mathfrak{g})$ introduced by Okado and Yamane, where $\mathfrak{g}$ is a complex simple Lie algebra, and all parameters lie in general position. We…
This paper computes the Dirac cohomology $H_D(\pi)$ of irreducible unitary Harish-Chandra modules $\pi$ of complex classical groups viewed as real reductive groups. More precisely, unitary representations with nonzero Dirac cohomology are…
A celebrated theorem of Harich-Chandra asserts that all invariant eigendistributions on a semisimple Lie group are locally integrable functions. We show that this result is a consequence of an algebraic property of a holonomic D-module…
In this paper, we classify all simple jet modules for the Neveu-Schwarz algebra $\widehat{\mathfrak{k}}$ and its contact subalgebra $\mathfrak{k}^+$. Based on these results, we give a classification of simple Harish-Chandra modules for…
In the case of cyclic quiver we prove that the deformed Harish-Chandra map whose existence was conjectured by Etingof and Ginzburg is well defined. As an application we prove Kirillov-type formula for the cyclotomic Bessel function.
In this article we consider the centre of the reduced enveloping algebra of the Lie algebra of a reductive algebraic group in very good characteristic p > 2. The Harish-Chandra centre maps to the centre of each reduced enveloping algebra…
Building on previous work of Kollar, Ein, Lazarsfeld, and Hacon, we show that ample divisors of low degree on an abelian variety have mild singularities in case the abelian variety is simple or the degree of the polarization is two.
Consider the character of an irreducible admissible representation of a p-adic reductive group. The Harish-Chandra-Howe local expansion expresses this character near a semisimple element as a linear combination of Fourier transforms of…
The paper is on the vanishing topology of singular Milnor fibres of holomorphic families of arbitrary square, symmetric and skew-symmetric matrices with sufficiently many parameters. We define vanishing cycles on such fibres, prove an…
The irreducible characters of a finite reductive group are partitioned into Harish-Chandra series that are labelled by cuspidal pairs. In this note, we describe how one can algorithmically calculate those cuspidal pairs using results of…