Related papers: Borel-Weil Theorem for Algebraic Supergroups

We show that semi-simple lie algebras can be characterized by their maximal nilpotent subalgebra, which is the same as the nilpotent radical of a Borel subalgebra.

This article deals with computing the cohomology of Schur functors applied to tautological bundles on super Grassmannians. We show that in a range of cases, the cohomology is a free module over the cohomology of the structure sheaf and that…

Given an elliptic curve defined over a number field $F$, we study the algebraic structure and prove a control theorem for Wuthrich's fine Mordell--Weil groups over a $\mathbb{Z}_p$-extension of $F$, generalizing results of Lee on the usual…

Controlled $K$-theory is used to show that algebraic $K$-theory of virtually abelian groups is described by an assembly map defined using possibly-infinite hyperelementary subgroups. The Farrell-Jones summand (coming from infinite…

We begin an investigation of supersymmetric theories based on exceptional groups. The flat directions are most easily parameterized using their correspondence with gauge invariant polynomials. Symmetries and holomorphy tightly constrain the…

For a given orthonormal basis $(f_n)$ on a probability measure space, we want to describe all Markov operators which have the $f_n$ as eigenvectors. We introduce for that what we call the hypergroup property. We study this property in three…

A subgroup $R$ of a finite group $G$ is weakly subnormal in $G$ if $R$ is not subnormal in $G$ but it is subnormal in every proper overgroup of $R$ in $G$. In this paper, we first classify all finite groups $G$ which contains a weakly…

We construct a gerbe over a complex reductive Lie group G attached to an invariant bilinear form on a maximal diagonalizable subalgebra which is Weyl group invariant and satisfies a parity condition. By restriction to a maximal compact…

We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra.…

This paper is a resolution of three related problems proposed by Yu. I. Manin and V. Kac for the so-called {\it{exceptional}} Lie superalgebras F(4) and G(3). The first problem posed by Kac (1978) is the problem of finding character and…

Global Weyl modules for generalized loop algebras $\lie g\tensor A$, where $\lie g$ is a simple finite dimensional Lie algebra and A is a commutative associative algebra were defined, for any dominant integral weight $\lambda$, by…

We study a semisimple extension of a Takiff superalgebra which turns out to have a remarkably rich representation theory. We determine the blocks in both the finite-dimensional and BGG module categories and also classify the Borel…

We construct quantization of semisimple conjugacy classes of the exceptional group $G=G_2$ along with and by means of their exact representations in highest weight modules of the quantum group $U_q(\mathfrak{g})$. With every point $t$ of a…

For any finitely generated abelian group $Q$, we reduce the problem of classification of $Q$-graded simple Lie algebras over an algebraically closed field of "good" characteristic to the problem of classification of gradings on simple Lie…

Let $G$ be a connected semi-simple group defined over and algebraically closed field, $T$ a fixed Cartan, $B$ a fixed Borel containing $T$, $S$ a set of simple reflections associated to the simple positive roots corresponding to $(T,B)$,…

We define global and local Weyl modules for $q \otimes A$, where $q$ is the queer Lie superalgebra and $A$ is an associative commutative unital $\mathbb{C}-$algebra. We prove that global Weyl modules are universal highest weight objects in…

Let $G$ be a simply connected semisimple algebraic group with Lie algebra $\mathfrak g$, let $G_0 \subset G$ be the symmetric subgroup defined by an algebraic involution $\sigma$ and let $\mathfrak g_1 \subset \mathfrak g$ be the isotropy…

We define an algebraic group over a group $G$ to be a variety - that is, a subset of $G^d$ defined by equations over $G$ - endowed with a group law whose coordinates can be expressed as word maps. In the case where $G$ is a torsion-free…

Let V(KG) be a normalised unit group of the modular group algebra of a finite p-group G over the field K of p elements. We introduce a notion of symmetric subgroups in V(KG) as subgroups invariant under the action of the classical…

Using combinatorial properties of symmetric polynomials, we compute explicitly the Soergel modules for some permutations whose corresponding Schubert varieties are rationally smooth. We build from them diagram algebras whose module…