Related papers: Gaiotto conjecture for $Rep_q(GL(N-1|N))$

Let $E/F$ be a quadratic extension of p-adic fields. We prove that every smooth irreducible ladder representation of the group $GL_n(E)$ which is contragredient to its own Galois conjugate, possesses the expected distinction properties…

Let $F$ be a non-archimedean local field with residue field $\mathbb{F}_q$ and let $G = GL_{2/F}$. Let $\mathbf{q}$ be an indeterminate and let $H^{(1)}(\mathbf{q})$ be the generic pro-p Iwahori-Hecke algebra of the group $G(F)$. Let…

We explicate the deep Riemann hypothesis for the general linear group $\mathrm{GL}_{n}$ on the convergence of normalised Euler products of standard $L$-functions on the critical line. It conditionally improves upon the error term in the…

We give a skein theoretic proof the Reshetikhin hook length formula for quantum dimension for the quantum group U_q(sl(N)).

The importance of symmetries has recently been recognized in quantum machine learning from the simple motto: if a task exhibits a symmetry (given by a group $\mathfrak{G}$), the learning model should respect said symmetry. This can be…

We find all irreducible hypergeometric sheaves whose geometric monodromy group is finite, almost quasisimple and has the projective special linear group $PSL_n(q)$ with $n\geq 3$ as a composition factor. We use the classification of…

We construct finite-dimensional irreducible representations of two quantum algebras related to the generalized Lie algebra $\ssll (2)_q$ introduced by Lyubashenko and the second named author. We consider separately the cases of $q$ generic…

Recently, motivated by supersymmetric gauge theory, Cachazo, Douglas, Seiberg, and Witten proposed a conjecture about finite dimensional simple Lie algebras, and checked it in the classical cases. We prove the conjecture for type G_2, and…

The relative trace formula of Jacquet-Rallis (for unitary groups or general linear groups) is an identity between periods of automorphic representations and geometric distributions. In this paper, we prove the transfer between all geometric…

We establish a Gelfand-Naimark-Segal construction which yields a correspondence between cyclic unitary representations and positive definite superfunctions of a general class of $\mathbb Z_2^n$-graded Lie supergroups.

We present and prove in detail a Poincare--Birkhoff--Witt commutator lemma for the quantum superalgebra U_q[gl(m|n)].

We give a new criterion for solvability of group equations, providing proofs of various generalizations of the Kervaire-Laudenbach conjecture for Connes-embeddable groups.

In this paper, we prove that the quantum toroidal algebra of gl_n is isomorphic to the double shuffle algebra of Feigin and Odesskii for the cyclic quiver. The shuffle algebra viewpoint will allow us to prove a factorization formula for the…

This is the second of a series of three papers where we prove the Gan--Gross--Prasad conjecture for Fourier--Jacobi periods on unitary groups and an Ichino--Ikeda type refinement. Our strategy is based on the comparison of relative trace…

We establish an explicit Plancherel decomposition for $\mathrm{GL}_n(F)\backslash \mathrm{GL}_n(E)$ where $E/F$ is a quadratic extension of local fields of characteristic zero by making use of a local functional equation for Asai…

We formulate and discuss two conjectures concerning recursive formulae for Branson's $Q$-curvatures. The proposed formulae describe all $Q$-curvatures on manifolds of all even dimensions in terms of respective lower order $Q$-curvatures and…

The relative Novikov conjecture states that the relative higher signatures of manifolds with boundary are invariant under orientation-preserving homotopy equivalences of pairs. In this paper, we study the relative Baum-Connes assembly map…

Let $X$ be a smooth projective curve of genus $\geq2$ over a number field. A natural variant of Grothendieck's Section Conjecture postulates that every section of the fundamental exact sequence for $X$ which everywhere locally comes from a…

In this article, we generalize Duflo's conjecture to understand the branching laws of non-discrete series. We give a unified description on the geometric side about the restriction of an irreducible unitary representation $\pi$ of…

We present state sums for quantum link invariants arising from the representation theory of $U_q(\mathfrak{gl}_{N|M})$. We investigate the case of the $N$-th exterior power of the standard representation of $U_q(\mathfrak{gl}_{N|1})$ and…