Related papers: A branching law for subgroups fixed by an involuti…

We begin with recalling the correspond theorem of induced modules and global sections of vector bundles. After that, we give a generalization of this theorem. Finally, we apply the result to branching laws, and give some concrete examples.

We establish branching rules between some Iwahori-Hecke algebra of type B and their subalgebras which are defined as fixed subalgebras by involutions including Goldman involution. The Iwahori-Hecke algebra of type D is one of such fixed…

In this note, we formulate and prove branching rules of simple polynomial modules for the Lie superalgebra $\mathfrak{gl}(m|n)$. Our branching rules depend on the conjugacy class of the Borel subalgebra. A Gelfand-Tsetlin basis of a…

M. Brion proved a convexity result for the moment map image of an irreducible subvariety of a compact integral Kaehler manifold preserved by the complexification of the Hamiltonian group action. V. Guillemin and R. Sjamaar generalized this…

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…

We find the explicit branching laws for the restriction of minimal holomorphic representations to symmetric subgroups in the case where the restriction is discretely decomposable. For holomorphic pairs the minimal holomorphic representation…

We consider the Ext-analogues of branching laws of representations for a group to its subgroups in the context of $p$-adic groups.

This paper generalizes the GGP conjectures which were earlier formulated for tempered or more generally generic L-packets to Arthur packets, especially for the nongeneric L-packets arising from Arthur parameters. The paper introduces the…

A general structure theorem on higher order invariants is proven. For an arithmetic group, the structure of the corresponding Hecke module is determined. It is shown that the module does not contain any irreducible submodule. This explains…

We prove a local Gan-Gross-Prasad conjecture on predicting the branching law for the non-tempered representations of general linear groups in the case of non-Archimedean field. We also generalize to Bessel and Fourier-Jacobi models and…

The main theorem of Galois theory states that there are no finite group-subgroup pairs with the same invariants. On the other hand, if we consider complex linear reductive groups instead of finite groups, the analogous statement is no…

This note outlines the Borel-Weil-Bott theory for (arbitrary-genus) flag varieties of loop groups, following ideas of G. Segal. Recent revivalist interest in the "WZW fusion rules" suggests that my original (CMP 1995) treatment of the…

We generalize the classical semiregularity theorem of Buchweitz and Flenner to the setting of noncommutative algebraic geometry, with group actions. This applies in particular to twisted derived categories, in which case it answers a…

In this paper we introduce a group invariant version of the wellknown Ekeland variational principle. To achieve this, we defne the concept of convexity with respect to a group and establish a version of the theorem within this framework.…

Classical invariant theory establishes a systematic correspondence between algebraic and smooth invariants for compact and reductive Lie groups. However, the extension of these results to non-compact and non-reductive regimes remains a…

All indecomposable finite-dimensional representations of the homogeneous Galilei group which when restricted to the rotation subgroup are decomposed to spin 0, 1/2 and 1 representations are constructed and classified. These representations…

We treat the convergence of Carleman linearization of nonlinear evolutionary equations through the approximation theory of strongly continuous semigroups, by Carleman embedding the underlying nonlinear semigroups as linear semigroups.…

Let G be a simple algebraic group over C with the Weyl group W. For a unipotent element u of G, let B_u be the variety of Borel subgroups of G containing u. Let L be a Levi subgroup of a parabolic subgroup of G with the Weyl subgroup W_L.…

We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly non-reflexive and non-separable spaces. The pivoting point is to establish a novel variational structure, based…

Consider a sequence of polynomials of bounded degree evaluated in independent Gaussian, Gamma or Beta random variables. We show that, if this sequence converges in law to a nonconstant distribution, then (i) the limit distribution is…