Related papers: The Howe duality conjecture: quaternionic case
The first goal of this paper is to provide an abstract framework in which to formulate and study local duality in various algebraic and topological contexts. For any stable $\infty$-category $\mathcal{C}$ together with a collection of…
We prove a nonsemisimple quantum version of Howe's duality with the rank 2n symplectic and the rank 2 special linear group acting on the exterior algebra of type C. We also discuss the first steps towards the symplectic analog of harmonic…
We provide formulas for the denominator and superdenominator of a basic classical type Lie superalgebra for any set of positive roots. We establish a connection between certain sets of positive roots and the theory of reductive dual pairs…
We give a new combinatorial interpretation of Howe dual pairs of the form $(\g,{\rm Sp}_{2\ell})$, where $\g$ is a Lie (super)algebra of classical type. This is done by establishing a symplectic analogue of the RSK algorithm associated to…
We use the theta lifts between Mp(2) and PD to study the distinction problems for the pair (Mp(2,E), SL(2,F )), where E is a quadratic field extension over a nonarchimedean local field F of characteristic zero and D is a quaternion algebra.…
Let $F$ be a $p$-adic field and $E/F$ be a quadratic extension. In this paper, we prove the local converse theorem for generic representations of $\textrm{U}_{E/F}(2,2)$ if $E/F$ is unramified or the residue characteristic of $F$ is odd.…
In this article we prove a Howe correspondence for a family of representations of sl(2n), which was introduced by Benkart, Britten, and Lemire.
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.…
The Askey-Wilson algebra and its relatives such as the Racah and Bannai-Ito algebras were initially introduced in connection with the eponym orthogonal polynomials. They have since proved ubiquitous. In particular they admit presentations…
The objective of this paper is to introduce and study completions and local homology of comodules over Hopf algebroids, extending previous work of Greenlees and May in the discrete case. In particular, we relate module-theoretic to…
Over a non-archimedean local field of characteristic zero, we prove the multiplicity preservation for orthogonal-symplectic dual pair correspondences and unitary dual pair correspondences.
An proof of Poincare Duality with local coefficients and with compact support is provided. The proof does not require Sheaf Theory or anything equivalent and is thus more accessible for the general audience.
We investigate a new property of nets of local algebras over 4-dimensional globally hyperbolic spacetimes, called punctured Haag duality. This property consists in the usual Haag duality for the restriction of the net to the causal…
We explicitly develop a quaternionic version of the electroweak theory, based on the local gauge group $U(1, q)_{L}\mid U(1, c)_{Y}$. The need of a complex projection for our Lagrangian and the physical significance of the anomalous scalar…
Extending Sellers' result, Das et al. recently proved some congruence results for generalized overcubic partitions using theta functions and posed some related conjectures. In this paper, we provide a combinatorial proof of a result in…
v2: An additional assumption was added in Theorem 4.8. In order to show that a connected abelian group is admissible on the site of locally compact spaces we must in addition assume that it is locally topologically divisible. This condition…
We study the functoriality of the local theta correspondence for classical $p$-adic groups. This is realized via the adaptation of the Adams conjecture to ABV-packets. We provide evidence for the conjecture, especially in the case of…
Among diversity of frameworks and constructions introduced in Loewner Theory by different authors, one can distinguish two closely related but still different ways of reasoning, which colloquially may be described as "increasing" and…
We establish classical and categorical Howe dualities between the Lie superalgebras $\mathfrak{p}(m)$ and $\mathfrak{p}(n)$, for $m,n \geq 1$. We also describe a presentation via generators and relations as well as a Kostant…
We first give a bijective proof of Gould's identity in the model of binary words. Then we deduce Rothe's identity from Gould's identity again by a bijection, which also leads to a double-sum extension of the $q$-Chu-Vandermonde formula.