Related papers: A proof of the Howe duality conjecture

Given a real irreducible dual pair there is an integral kernel operator which maps the distribution character of an irreducible admissible representation of the group with the smaller or equal rank to an invariant eigendistribution on the…

We establish an Esakia duality for the categories of temporal Heyting algebras and temporal Esakia spaces. This includes a proof of contravariant equivalence and a congruence/filter/closed-upset correspondence. We then study two notions of…

This article has a twofold purpose. First, by recent works of Kaletha and Loke-Ma, we give an explicit description of the local theta correspondence between regular supercuspidal representations in the equal rank symplectic-orthogonal case.…

We show that very general hypersurfaces in odd-dimensional simplicial projective toric varieties verifying a certain combinatorial property satisfy the Hodge conjecture (these include projective spaces). This gives a connection between the…

We proved a new Siegel-Weil formula for orthogonal and symplectic groups, which will be used later to prove a generalization of Siegel-Weil formula for loop groups.

We prove Haag duality for conelike regions in the ground state representation corresponding to the translational invariant ground state of Kitaev's quantum double model for finite abelian groups. This property says that if an observable…

Let $G$ be a classical group $\GL(n)$, $\oU(n)$, $\oO(n)$ or $\Sp(2n)$, over a non-archimedean local field of characteristic zero. Let $\pi$ be an irreducible admissible smooth representation of $G$. It is well known that the contragredient…

In this note we clarify the relationship between the local and global definitions of dual pairs in Poisson geometry. It turns out that these are not equivalent. For the passage from local to global one needs a connected fiber hypothesis…

We continue our work on understanding Howe correspondences by using theta representations from p-adic groups to compact groups. We prove some results for unitary theta representations of compact groups with respect to the induction and…

In a previous paper we formulated an analogue of the Ichino-Ikeda conjectures for Whittaker-Fourier coefficients of cusp forms on quasi-split groups, as well as the metaplectic group of arbitrary rank. In this paper we reduce the conjecture…

This paper provides a construction of the unipotent representations for classical complex groups in terms of the Theta correspondence as introduced and studied by R. Howe. The K-type structure of unipotent representations is obtained as a…

The duality is a fundamental property of the finite multiple harmonic sums (MHS). In this paper, we prove a duality result for certain generalizations of MHS which appear naturally as the differences of MHS. We also prove a formula for the…

We show that dualising transfer maps in Hochschild cohomology of symmetric algebras commutes with Tate duality. This extends a well-known result in group cohomology.

In this paper we give an elementary proof of the local sum conjecture in two dimensions. In a remarkable paper [CMN, arXiv:1810.11340], this conjecture has been established in all dimensions using sophisticated, powerful techniques from a…

In this paper, we present a simple combinatorial proof of a Weyl type formula for hook Schur polynomials, which has been obtained by using a Kostant type cohomology formula for $\frak{gl}_{m|n}$. In general, we can obtain in a combinatorial…

A geometric interpretation of the duality between two real forms of the complex trigonometric Ruijsenaars-Schneider system is presented. The phase spaces of the systems in duality are viewed as two different models of the same reduced phase…

We give a new and simpler proof of a result of Hopkins and Gross relating Brown-Comenetz duality to Spanier-Whitehead duality in the K(n)-local stable homotopy category.

We prove certain duality properties and present recurrence relations for a four-parameter family of self-dual Koornwinder-Macdonald polynomials. The recurrence relations are used to verify Macdonald's normalization conjectures for these…

We find criteria ensuring that a local (holomorphic, real analytic, $C^1$) homeomorphism between the Julia sets of two given rational functions comes from an algebraic correspondence. For example, we show that if there is a local…

We consider weighted double Hurwitz numbers, with the weight given by arbitrary rational function times an exponent of the completed cycles. Both special singularities are arbitrary, with the lengths of cycles controlled by formal…