Related papers: Bounded multiplicity branching for symmetric pairs

For an essentially tame supercuspidal representation $\pi$ of a connected reductive $p$-adic group $G$, we establish two distinct and complementary sufficient conditions for the irreducible components of its restriction to a maximal compact…

We give criteria for real, complex and quaternionic representations to define s-representations, focusing on exceptional Lie algebras defined by spin representations. As applications, we obtain the classification of complex representations…

For fixed compact connected Lie groups H \subseteq G, we provide a polynomial time algorithm to compute the multiplicity of a given irreducible representation of H in the restriction of an irreducible representation of G. Our algorithm is…

For each irreducible finite dimensional representation of the Lie algebra $\mathfrak{sl}_2(\mathbb{C})$ of $2\times 2$ traceless matrices, an explicit uniform upper bound is given for the multiplicities in the cocharacter sequence of the…

Suppose a finite group acts on a scheme X and a finite-dimensional Lie algebra g. The corresponding equivariant map algebra is the Lie algebra M of equivariant regular maps from X to g. We classify the irreducible finite-dimensional…

We prove that if $\Sigma$ is a closed surface of genus at least 3 and $G$ is a split real semisimple Lie group of rank at least $3$ acting faithfully by isometries on a symmetric space $N$, then there exists a Hitchin representation…

The irreducible decomposition of a unitary representation often contains continuous spectrum when restricted to a non-compact subgroup. The author singles out a nice class of branching problems where each irreducible summand occurs…

We consider the following class of unitary representations $\pi $ of some (real) Lie group $G$ which has a matched pair of symmetries described as follows: (i) Suppose $G$ has a period-2 automorphism $\tau $, and that the Hilbert space…

We study the irreducible representations of simple algebraic groups in which some non-central semisimple element has at most one eigenvalue of multiplicity greater than 1. We bound the multiplicity of this eigenvalue in terms of the rank of…

Let $G$ be a split simply laced group defined over a $p$-adic field $F$. In this paper we study the restriction of the minimal representation of $G$ to various dual pairs in $G$. For example, the restriction of the minimal representation of…

In this note, we address a question raised by Kr\"otz on the classification of domains of holomorphy of irreducible admissible Banach representations for connected non-compact simple real Lie groups G. When G is not of Hermitian type, we…

Let $G_n=\mathrm{GL}_n(F)$ be the general linear group over a non-Archimedean local field $F$. We formulate and prove a necessary and sufficient condition on determining when \[ \mathrm{Hom}_{G_n}(\pi, \pi') \neq 0 \] for irreducible smooth…

Building on reduction theorems and dimension bounds for symmetric groups obtained in our earlier work, we classify the irreducible restrictions of representations of the symmetric and alternating groups to proper subgroups. Such…

We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of…

Let $E/F$ be a unramified quadratic extension of non-archimedean local fields of odd characteristic $p$, and $G$ be the unramified unitary group $U(2, 1)(E/F)$. For an irreducible smooth representation $\pi$ of $G$ over…

We classify the finite-dimensional irreducible linear representations of the Baumslag-Solitar groups BS(p,q) = < a, b | a b^p = b^q a > for relatively prime p and q. The general strategy of the argument is to consider the matrix group given…

We discuss recent developments on branching problems of irreducible unitary representations $\pi$ of real reductive groups when restricted to reductive subgroups. Highlighting the case where the underlying $(g,K)$-modules of $\pi$ are…

We determine the irreducible representations of alternating and symmetric groups and their universal central extensions that contain a non-scalar element with all but one eigenvalues of multiplicity 1. The ground field is algebraically…

We give an example of a semisimple symmetric space $G/H$ and an irreducible representation of $G$ which has multiplicity 1 in $L^2(G/H)$ and multiplicity 2 in $C^\infty(G/H)$.

In this note we introduce the concept of a semi-bounded unitary representations of an infinite-dimensional Lie group $G$. Semi-boundedness is defined in terms of the corresponding momentum set in the dual $\g'$ of the Lie algebra $\g$ of…