Related papers: Decomposition of reductive regular prehomogeneous …

Let $G$ be a split reductive group over a local field $\bK$, and let $G((t))$ be the corresponding loop group. In \cite{GK} we have introduced the notion of a representation of (the group of $\bK$-points) of $G((t))$ on a pro-vector space.…

Let $G$ be a connected complex Lie group. A real form of $G$ is a closed subgroup $H\subset G$ whose Lie algebra $\mathfrak{h}$ is a real form of the Lie algebra $\mathfrak{g}$ of $G$. A pair $(G,H)$ of this type is reductive, and the…

We study the parabolically induced complex representations of the unitary group in 5 variables, $ U(5), $ defined over a p-adic field. Let $ F $ be a p-adic field. Let $ E : F $ be a field extension of degree two. Let $ Gal(E : F ) = \{ 1 ,…

Let G be an exceptional algebraic group defined over an algebraically closed field k of characteristic p>0 and let H be a subgroup of G. Then following Serre we say H is G-completely reducible or G-cr if, whenever H is contained in a…

With each resonance of the Laplacian acting on the compactly supported sections of a homogeneous vector bundle over a Riemannian symmetric space of the non-compact type, One can associate a residue representation. The purpose of this paper…

We describe a type of n-point function associated to strongly regular vertex operator algebras V and their irreducible modules. Transformation laws with respect to the Jacobi group are developed for 1-point functions. For certain elements…

Let $G$ be a reductive group acting on a path algebra $kQ$ as automorphisms. We assume that $G$ admits a graded polynomial representation theory, and the action is polynomial. We describe the quiver $Q_G$ of the smash product algebra $kQ\#…

For a simple vertex operator algebra $V$ and a finite automorphism group $G$ of $V$ then $V$ is a direct sum of $V^{\chi}$ where $\chi$ are irreducible character of $G$ and $V^{\chi}$ is the subspace of $V$ which $G$ acts according to the…

We prove a decomposition theorem for irreducible components of Grassmannians of submodules, as well as for other schemes arising from representation theory, thus generalising the result of Crawley-Boevey and Schroer for module varieties.…

Let $V$ be a simple vertex operator algebra, and $G$ a finite automorphism group of $V$ such that $V^G$ is regular. The definition of entries in $S$-matrix on $V^G$ is discussed, and then is extended. The set of $V^G$-modules can be…

$H$ is called a $G$-subgroup of a hyperbolic group $G$ if for any finite subset $M\subset G$ there exists a homomorphism from $G$ onto a non-elementary hyperbolic group $G_1$ that is surjective on $H$ and injective on $M$. In his paper in…

Let G be a simply connected simple algebraic group over an algebraically closed field K of characteristic p>0 with root system R, and let ${\mathfrak g}={\cal L}(G)$ be its restricted Lie algebra. Let V be a finite dimensional ${\mathfrak…

Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of…

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…

This paper proposes a new approach to deriving a finite particle content, suitable for the construction of a gauge theory. Specifically, the outlined construction generates a finite set of irreducible gauge representations, which are…

Let $X\subset \mathbb {P}^r$ be an integral and non-degenerate variety. For any $q\in \mathbb {P}^r$ let $r_X(q)$ be its $X$-rank and $\mathcal {S} (X,q)$ the set of all finite subsets of $X$ such that $|S|=r_X(q)$ and $q\in \langle…

We consider the structure of algebra of operators, acting in $n-$fold tensor product space, which are partially transposed on the last term. Using purely algebraical methods we show that this algebra is semi-simple and then, considering its…

We study the isotropic Quot schemes $IQ_e (V)$ parameterizing degree $e$ isotropic subsheaves of maximal rank of an orthogonal bundle $V$ over a curve. The scheme $IQ_e (V)$ contains a compactification of the space $IQ^o_e (V)$ of degree…

We find all irreducible hypergeometric sheaves whose geometric monodromy group is finite, almost quasisimple and has the projective special linear group $PSL_n(q)$ with $n\geq 3$ as a composition factor. We use the classification of…

We show that the irreducible components of any moduli space of semistable representations of a special biserial algebra are always isomorphic to products of projective spaces of various dimensions. This is done by showing that irreducible…