Related papers: On the reductive monoid associated to a parabolic …

Let $\mathbf{P}$ be a parabolic subgroup with Levi $\mathbf{M}$ of a connected reductive group defined over a locally compact non-archimedean field $F$. Given a certain compact open subgroup $\Gamma$ of $\mathbf{P}(F)$, this note proves…

Maximal parabolic subalgebras of untwisted affine Kac-Moody algebras were studied in the context of Borel-de Siebenthal theory in [13], where they were realized as certain equivariant map algebras with a non-free abelian group action. In…

Let $\mathfrak{g}$ be a simple Lie algebra defined over an algebraically closed field $k$ of characteristic $p$. Fix an integer $r>1$ and suppose that $V_1,\ldots,V_r$ are irreducible closed subvarieties of $\mathfrak{g}$. Let…

Let $k$ be an algebraically closed field of positive characteristic, $G$ a reductive group over $k$, and $V$ a finite dimensional $G$-module. Let $P$ be a parabolic subgroup of $G$, and $U_P$ its unipotent radical. We prove that if…

We establish a novel approach to computing $G$-equivariant cohomology for a finite group $G$, and demonstrate it in the case that $G = C_{p^n}$. For any commutative ring spectrum $R$, we prove a symmetric monoidal reconstruction theorem for…

For an inner form $\mathrm{G}$ of a general linear group or classical group over a non-archimedean local field of odd residue characteristic, we decompose the category of smooth representations on $\mathbb{Z}[\mu_{p^{\infty}},1/p]$-modules…

Consider a complex projective space with its Fubini-Study metric. We study certain one parameter deformations of this metric on the complement of an arrangement (=a finite union of hyperplanes) whose Levi-Civita connection is of Dunkl…

We investigate positive-dimensional closed reductive subgroups of almost simple algebraic groups containing a regular unipotent element. Our main result states that such subgroups do not lie inside proper parabolic subgroups unless possibly…

We study the semisimplification of the full karoubian subcategory generated by the irreducible finite dimensional representations of the algebraic supergroup $GL(m|n)$ over an algebraically closed field of characteristic zero. This…

Let $\overline{M}=\overline{G}/\overline{H}$ be a homogeneous Riemannian manifold. Given a Lie subgroup $G\subset \overline{G}$ and a reductive decomposition of the homogeneous structure of $\overline{M}$, we analyze a canonical reductive…

Let $F$ be a locally compact non-Archimedean field, and $\bf G$ a connected quasi-split reductive group over $F$. We are interested in complex irreducible smooth generic representations $\pi$ of ${\bf G}(F)$. When $F$ has positive…

Given a compact Kaehler manifold, we consider the complement U of a divisor with normal crossings. We study the variety of unitary representations of the fundamental group of U with certain restrictions related to the divisor. We show that…

Let $G$ be a semisimple, simply connected algebraic group over an algebraically closed field of characteristic zero. We prove that the $\infty$-category of D-modules on the loop group of $G$ is equivalent to the monoidal colimit of the…

We develop a new method for obtaining branching rules for affine Kac-Moody Lie algebras at negative integer levels. This method uses fusion rules for vertex operator algebras of affine type. We prove that an infinite family of ordinary…

In this paper we prove equivalences of categories relating the derived category of a block of the category of representations of a connected reductive algebraic group over an algebraically closed field of characteristic $p$ bigger than the…

We study representations of the classical infinite dimensional real simple Lie groups $G$ induced from factor representations of minimal parabolic subgroups $P$. This makes strong use of the recently developed structure theory for those…

Consider a reductive group G over a non-archimedean local field. The Galois group Gal(C/Q) acts naturally on the category of smooth complex G-representations. We prove that this action stabilizes the class of standard modules. This…

We describe irreducible representations and character formulas of the Renner monoids for reductive monoids, which generalizes the Munn-Solomon representation theory of rook monoids to any Renner monoids. The type map and polytope associated…

For a quasi-split connected reductive group $G$ over a local field $F$ we define a compact abelian group $\tilde\pi_1(G)$ and an extension $1 \to \tilde\pi_1(G) \to G(F)_\infty \to G(F) \to 1$ of topological groups equipped with a splitting…

For a monoid $M$, we denote by $\mathbb G(M)$ the group of units, $\mathbb E(M)$ the submonoid generated by the idempotents, and $\mathbb G_L(M)$ and $\mathbb G_R(M)$ the submonoids consisting of all left or right units. Writing $\mathcal…