Related papers: Branching of metaplectic representation of $Sp(2, …

We solve a classical problem of centrality of symplectic $\mathrm K_2$, namely we show that for an arbitrary commutative ring $R$, $l\geq3$ the symplectic Steinberg group $\mathrm{StSp}(2l,\,R)$ as an extension of the elementary symplectic…

The semisimple subalgebras of the rank $2$ symplectic Lie algebra $\mathfrak{sp}(4,\mathbb{C})$ are well-known, and we recently classified its Levi decomposable subalgebras. In this article, we classify the solvable subalgebras of…

We determine the characters of SL(2) representations of groups and surface groups.

We prove that all lattices of Sp(2n,R), except those commensurable with Sp(4k+2,Z) when n=2k+1, contain the image of infinitely many mapping class group orbits of Zariski-dense maximal representation that are continuous deformations of…

If $(G_1, G_2)$ is a dual reductive pair of type I in $Sp(W)$, it is known that the degree $8$ metaplectic cover of $Sp(W)$ splits over $G_1G_2$, with one obvious exception. In this paper we replace $G_1G_2$ by a larger subgroup obtained…

In this paper we consider the restriction of a unitary irreducible representation of type $A_{\mathfrak q}(\lambda)$ of $GL(4,{\mathbb R})$ to reductive subgroups $H$ which are the fixpoint sets of an involution. We obtain a formula for the…

In this paper we consider (polynomial) solution spaces for the symplectic Dirac operator (with a focus on $1$-homogeneous solutions). This space forms an infinite-dimensional representation space for the symplectic Lie algebra…

We generalize the Shimura-Waldspurger correspondence, which describes the generic part of the automorphic discrete spectrum of the metaplectic group $\mathrm{Mp}_2$, to the metaplectic group $\mathrm{Mp}_{2n}$ of higher rank. To establish…

In this paper we consider the analytic continuation of the weighted Bergman spaces on the Lie ball $$\mathscr{D}=SO(2,n)/S(O(2) \times O(n))$$ and the corresponding holomorphic unitary (projective) representations of SO(2,n) on these…

Let $F$ be a $p$-adic field of characteristic zero and odd residual characteristic. Let $\mathbf{Sp}_{2n}(F)$ denote the symplectic group defined over $F$, where $n\geq 2$. We prove that the Speh representations $\mathcal{U}(\delta,2)$,…

We construct the representations of affine sl(2,R) starting from the unitary representations of the loop ax+b-group. Our approach involves a combinatorial analysis of the correlation functions of the generators and renormalization of the…

In this paper we study the sp(2m)-invariant Dirac operator Ds which acts on symplectic spinors, from an orthogonal point of view. By this we mean that we will focus on the subalgebra so(m), as this will allow us to derive branching rules…

In the framework of McKay correspondence we determine, for every finite subgroup $\Gamma$ of $\mathbf{SL}_4\mathbb{C}$, how the finite dimensional irreducible representations of $\mathbf{SL}_4\mathbb{C}$ decompose under the action of…

We give the decomposition into irreducible representations of the restriction to a maximal compact subgroup of any irreducible depth-zero supercuspidal representation of $\mathrm{SL}(2,F)$ when $F$ is a local nonarchimedean field of…

We construct and study the holomorphic discrete series representation and the principal series representation of the symplectic group $\mathrm{Sp}(2n,F)$ over a $p$-adic field $F$ as well as a duality between some sub-representations of…

Let $\mathfrak{o}$ be a compact discrete valuation ring with maximal ideal $\mathfrak{p}$ such that the finite residue field $\mathfrak{o}/\mathfrak{p}$ has characteristic $p.$ For $r\geq2$ and $p=2,$ we obtain the branching rules for the…

We determine the irreducible 2-modular representations of the symplectic group $G=Sp_{2n}(2)$ whose restriction to every abelian subgroup has a trivial constituent. A similar result is obtained for maximal tori of $G$. There is significant…

For a positive integer $g$, let $\mathrm{Sp}_{2g}(R)$ denote the group of $2g \times 2g$ symplectic matrices over a ring $R$. Assume $g \ge 2$. For a prime number $\ell$, we give a self-contained proof that any closed subgroup of…

Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group $SL(2,C)\otimes SL(2,C)$, composed of local operators acting on the binary…

We investigate the theory of induction in the setting of doubles of coideal $*$-subalgebras of compact quantum group Hopf $*$-algebras. We then exemplify parts of this theory in the particular case of quantum $SL(2,\mathbb{R})$, and compute…