Related papers: A proof of the Howe duality conjecture

We provide various counter-examples to the long-standing so-called "Omnibus Conjecture" in Rational Homotopy Theory. That is, we show that a space with finite dimensional even-degree rational cohomology and finite dimensional spherical…

A combinatorial group-theoretic hypothesis is presented that serves as a necessary and sufficient condition for a union of connected Cockcroft two-complexes to be Cockcroft. This hypothesis has a component that can be expressed in terms of…

We explain how Lie superalgebras of types gl and osp provide a natural framework generalizing the classical Schur and Howe dualities. This exposition includes a discussion of super duality, which connects the parabolic categories O between…

Matlis duals of local cohomology modules are investigated with respect to many different topics (see section 0 - Introduction). One of these topics are complete intersections - see Corollary 1.1.4.

We prove some combinatorial identities using the Polya urn and the closely related Hoppe urn.

The Hikita conjecture relates the coordinate ring of a conical symplectic singularity to the cohomology ring of a symplectic resolution of the dual conical symplectic singularity. We formulate a quantum version of this conjecture, which…

We study model transition for representations occurring in the local theta correspondence between split even special orthogonal groups and symplectic groups, over a non-archimedean local field of characteristic zero.

In the paper we complete a case by case proof of Reeder's Conjecture started in our previous work, proving the conjecture for simple Lie algebras of type $D$ and for the exceptional cases.

We study the behavior of Galois periods under the local theta correspondence for even orthogonal and symplectic groups. Specifically, we compare their multiplicities and construct explicit transfer maps. Furthermore, we establish both an…

We develop a geometric approach toward an interplay between a pair of quantum Schur algebras of arbitrary finite type. Then by Beilinson-Lusztig-MacPherson's stabilization procedure in the setting of partial flag varieties of type A (resp.…

We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.

We introduce and study the notion of contact dual pair adopting a line bundle approach to contact and Jacobi geometry. A contact dual pair is a pair of Jacobi morphisms defined on the same contact manifold and satisfying a certain…

A sub-relation of the $\Theta$-correspondence called the \emph{$\eta$-correspondence} is defined by Gurevich-Howe for a finite reductive dual pair in stable range. In this paper we propose an extension of the correspondence to general…

In previous papers we formulated an analogue of the Ichino--Ikeda conjectures for Whittaker--Fourier coefficients of automorphic forms on classical group and the metaplectic group. In the latter case we reduced the conjecture to a local…

For a Liouville domain $W$ satisfying $c_1(W)=0$, we propose in this note two versions of symplectic Tate homology $\underrightarrow{H}\underleftarrow{T}(W)$ and $\underleftarrow{H}\underrightarrow{T}(W)$ which are related by a canonical…

We compare two henselisations of a residually discrete valuation domain. Our constructive proof that a certain natural morphism is an isomorphism is also a proof in classical mathematics. Although this isomorphism is implicitly accepted as…

We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]

We give an equivalent form of the Twin prime conjecture relating to a symmetric property that is observed for terms present in a certain sequence of arithmetic progressions defined for a pair of co-prime integers.

Using Howe duality we compute explicitly Kostant-type homology groups for a wide class of representations of the infinite-dimensional Lie superalgebra $\hat{\frak{gl}}_{\infty|\infty}$ and its classical subalgebras at positive integral…

We prove that a certain cohomological residue associated to an ideal of pure dimension is annihilated exactly by the ideal. The cohomological residue is quite explicit and generalizes the classical local Grothendieck residue and the…