Related papers: Some branching laws for symmetric spaces

We analyze patterns of remnant discrete symmetries that arise from U(1)^N theories by spontaneous breaking. We describe a simple, geometrical way to understand these patterns and provide methods for identifying the discrete symmetries and…

We construct a subalgebra of the Hecke algebra of type A. This is a generalization of the group algebra of the alternating groups. All the equivalent classes of irreducible representations of the subalgebra and the q-analogue of the…

We give uniform formulas for the branching rules of level 1 modules over orthogonal affine Lie algebras for all conformal pairs associated to symmetric spaces. We also provide a combinatorial intepretation of these formulas in terms of…

For reductive symmetric spaces G/H of split rank one we identify a class of minimal parabolic subgroups for which certain cuspidal integrals of Harish-Chandra - Schwartz functions are absolutely convergent. Using these integrals we…

Let $F$ be a nonarchimedean local field of characteristic zero and odd residual characteristic. Let $X$ be the $p$-adic symmetric space $X = H \backslash G$, where $G = \mathbf{GL}_{2n}(F)$ and $H = \mathbf{GL}_n(F) \times…

In this paper we study the branching law for the restriction from $SU(n,m)$ to $SO(n,m)$ of the minimal representation in the analytic continuation of the scalar holomorphic discrete series. We identify the the group decomposition with the…

We prove the symmetric version of Kottman's theorem, that is to say, we demonstrate that the unit sphere of an infinite-dimensional Banach space contains an infinite subset $A$ with the property that $\|x\pm y\| > 1$ for distinct elements…

We find the branching laws for the classical pairs $\mathrm{GL}(m, \mathbb{C}) \subset \mathrm{GL}(n, \mathbb{C})$, $\mathrm{Sp}(2m, \mathbb{C}) \subset \mathrm{Sp}(2n, \mathbb{C})$, $\mathrm{SO}(q, \mathbb{C}) \subset \mathrm{SO}(p,…

We introduce a new class of symmetric space orbital integrals important for applications in certain relative trace formulas appearing in the theory of automorphic representations. We verify a fundamental lemma for $U_2\times…

We develop an algebraic approach to the branching of representations of the general linear Lie superalgebra $\mathfrak{gl}_{p|q}({\mathbb C})$, by constructing certain super commutative algebras whose structure encodes the branching rules.…

Nonlinear equations of $p$-branes in $D=(2p+1)$-dimensional Minkowski space are discussed. Presented are new exact solutions for a set of spinning $p$-branes with $p=2,3,...,(D-1)/2$ and the Abelian symmetries $U(1)\times U(1)\times...…

We prove Gaussian approximation theorems for specific $k$-dimensional marginals of convex bodies which possess certain symmetries. In particular, we treat bodies which possess a 1-unconditional basis, as well as simplices. Our results…

We classify the irreducible projective representations of symmetric and alternating groups of minimal possible and second minimal possible dimensions, and get a lower bound for the third minimal dimension. On the way we obtain some new…

We study the local behavior of special cycles on Shimura varieties for $\mathbf{U}(2, 1) \times \mathbf{U}(1, 1)$ in the setting of the Gan-Gross-Prasad conjectures at primes $\tau$ of the totally real field of definition of the unitary…

A prime geodesic theorem for singular geodesics in a locally symmetric space is proved. As an application, an asymptotic formula for units in number fields is given.

Consider the space B of complex $p\times q$ matrces with norm <1. There exists a standard one-parameter family $S_a$ of unitary representations of the pseudounitary group U(p,q) in the space of holomorphic functions on B (i.e. scalar…

We determine a set of primitive idempotents and the basic algebra of the restricted quantum group $\bar{U}_qsl_2(\mathbb{C})$. As a result, we can show the dimension of the space of symmetric linear functions of $\bar{U}_qsl_2(\mathbb{C})$…

In this paper we construct faithful representations of saturated fusion systems over discrete p-toral groups and use them to find conditions that guarantee the existence of unitary embeddings of p-local compact groups. These conditions hold…

We explore the diversity of subsymmetric basic sequences in spaces with a subsymmetric basis. We prove that the subsymmetrization $Su(T^*)$ of Tsirelson's original Banach space provides the first known example of a space with a unique…

We examine the solution of the constraints in spherically symmetric general relativity when spacetime has a flat spatial hypersurface. We demonstrate explicitly that given one flat slice, a foliation by flat slices can be consistently…