Related papers: Regular functions on spherical nilpotent orbits in…

Let $G=\mathrm{GL}_n(\mathbb{F})$, $\mathrm{O}_n(\mathbb{F})$, or $\mathrm{Sp}_{2n}(\mathbb{F})$ be one of the classical groups over an algebraically closed field $\mathbb{F}$ of characteristic $0$, let $\breve{G}$ be the MVW-extension of…

We show that spaces of Colombeau generalized functions with smooth parameter dependence are isomorphic to those with continuous parametrization. Based on this result we initiate a systematic study of algebraic properties of the ring…

The ring of symmetric functions can be implemented in the homology of \union_{a,b} Gr(a,a+b), the multiplicative structure being defined from the "direct sum" map. There is a natural circle action (simultaneously on all Grassmannians) under…

Classifying endotrivial kG-modules, i.e., elements of the Picard group of the stable module category for an arbitrary finite group G, has been a long-running quest. By deep work of Dade, Alperin, Carlson, Thevenaz, and others, it has been…

Let $\mathcal{M}$ be an atomless semifinite von Neumann algebra (or an atomic von Neumann algebra with all atoms having the same trace) acting on a (not necessarily separable) Hilbert space $H$ equipped with a semifinite faithful normal…

This is the author's second paper treating the double coset problem for classical groups. Let $G$ be an algebraic group over an algebraically closed field $K$. The double coset problem consists of classifying the pairs $H,J$ of closed…

This paper is a continuation of arXiv:1201.1102. We investigate the orbit closures for the class of representations of simple algebraic groups associated to various gradings on the simple Lie algebra of type $E_7$. The methods for…

We study extremal black hole solutions of the S3 model (obtained by setting S=T=U in the STU model) using group theoretical methods. Upon dimensional reduction over time, the S3 model exhibits the pseudo-Riemannian coset structure G/K with…

The main aim of this work is to construct several new families of proper biharmonic functions defined on open subsets of the classical compact simple Lie groups $\SU n$, $\SO n$ and $\Sp n$. We work in a geometric setting which connects our…

In this note we investigate the normality of closures of orthogonal and symplectic nilpotent orbits in positive characteristic. We prove that the closure of such a nilpotent orbit is normal provided that neither type d nor type e minimal…

For a (Reimannian) symmetric space $G/K$ of compact type, the natural action of $G$ on its complexification $G^{\mathbb C}/K^{\mathbb C}$ (which is an anti-Kaehler symmetric space) is one of the isometric actions called ``Hermann type…

The Springer resolution of the nilpotent cone of a semisimple Lie algebra has played an important role in representation theory. The nilpotent cone is equal to Spec R, where R is the ring of regular functions on the nilpotent cone. This…

Let G be a simple algebraic group over an algebraically closed field with Lie algebra g. Then the orbits of nilpotent elements of g under the adjoint action of G have been classified. We describe a simple algorithm for finding a…

We approach the topic of Classical group nilpotent orbits from the perspective of their moduli spaces, described in terms of Hilbert series and generating functions. We review the established Higgs and Coulomb branch quiver theory…

Let $G/K$ be an irreducible symmetric space where $G$ is a non-compact, connected Lie group and $K$ is a compact, connected subgroup. We use decay properties of the spherical functions to show that the convolution product of any $r=r(G/K)$…

Let $G$ be a reductive group over an algebraically closed field of positive characteristic $p$, good for the root system of $G$. The closures of $G$-orbits in the Hilbert nullcone of the coadjoint representation are conical affine Poisson…

The article gives the second part of the treatise on Regular Algebraic $K$-theory (Sections V & VI) of the author. Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected to (but different from)…

Let $G$ be a connected reductive algebraic group over an algebraically closed field ${\bf k}$ of characteristic not equal to 2, let $\B$ be the variety of all Borel subgroups of $G$, and let $K$ be a symmetric subgroup of $G$. Fixing a…

Let $G$ be a real simple Lie group, $\got g$ its Lie algebra. Given a nilpotent adjoint $G$-orbit $O$, the question is to determine the irreducible unitary representations of $G$ that we can associate to $O$, according to the orbit method.…

We show that, for a sheet or a Lusztig stratum S containing spherical conjugacy classes in a connected reductive algebraic group G over an algebraically closed field in good characteristic, the orbit space S/G is isomorphic to the quotient…