Related papers: Finite groups, smooth invariants, and isolated quo…

Let F be the flag variety of a complex semi-simple group G, let H be an algebraic subgroup of G acting on F with finitely many orbits, and let V be an H-orbit closure in F. Expanding the cohomology class of V in the basis of Schubert…

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…

Let G be a group and let W be an algebra over a field K. We will say that W is a G-graded twisted algebra if W can be written as a direct sum over the elements of G of one dimensional K-vector spaces. It is also assumed that W has no…

Let F be characteristic zero field, G a residually finite group and W a G-prime and PI F-algebra. By constructing G-graded central polynomials for W, we prove the G-graded version of Posner's theorem. More precisely, if S denotes all…

We develop a representation theoretic technique for detecting closed orbits that is applicable in all characteristics. Our technique is based on Kempf's theory of optimal subgroups and we make some improvements and simplify the theory from…

Let G be a finite group acting tamely on a proper reduced curve C over an algebraically closed field. We study the G-module structure on the cohomology groups of a G-equivariant locally free sheaf F on C, and give formulas of…

We investigate symmetric quotient algebras of symmetric algebras, with an emphasis on finite group algebras over a complete discrete valuation ring ${\mathcal O}$. Using elementary methods, we show that if an ordinary irreducible character…

In this note we first study regular $\mathbb{Z}$-graded local rings. We characterize commutative noetherian regular $\mathbb{Z}$-graded local rings in similar ways as in the usual local case. Then, we characterize graded isolated…

We study the quotient of a completion of a symmetric variety G/H under the action of H. We prove that this is isomorphic to the closure of the image of an isotropic torus under the action of the restricted Weyl group. In the case the…

Let G be a simple complex algebraic group. By using a notion of a G-category we define invariants of tangles with flat G-connections in their complements. We also show that quantized universal enveloping algebras at roots of unity provide…

Given a grading by an abelian group G on a semisimple Lie algebra L over an algebraically closed field of characteristic 0, we classify up to isomorphism the simple objects in the category of finite-dimensional G-graded L-modules. The…

The ring of invariant polynomials ${\mathbb C}[V]^G$ over a given finite dimensional representation space $V$ of a complex reductive group $G$ is known, by a famous theorem of Hilbert, to be finitely generated. The general proof being…

In this note, we prove that for any finite dimensional vector space $V$ over an algebraically closed field $k$, and for any finite subgroup $G$ of $GL(V)$ which is either solvable or is generated by pseudo reflections such that the $|G|$ is…

Let G be a connected reductive group. Recall that a G-variety X is called spherical if X is normal and a Borel subgroup of G has an open orbit on X. To a spherical homogeneous G-space one assigns certain combinatorial invariants: the weight…

Let $K$ be a field and $G$ be a group of its automorphisms endowed with the compact-open topology. There are many situations, where it is natural to study the category $Sm_K(G)$ of smooth (i.e. with open stabilizers) $K$-semilinear…

Let G be a simple algebraic group over an algebraically closed field k of bad characteristic. We classify the spherical unipotent conjugacy classes of G. We also show that if the characteristic of k is 2, then the fixed point subgroup of…

We prove a finite-dimensional covariant Stinespring theorem for compact quantum groups. Let G be a compact quantum group, and let T:= Rep(G) be the rigid C*-tensor category of finite-dimensional continuous unitary representations of G. Let…

Let $W$ be a finite-dimensional representation of a reductive algebraic group $G$. The invariant Hilbert scheme $\mathcal{H}$ is a moduli space that classifies the $G$-stable closed subschemes $Z$ of $W$ such that the affine algebra $k[Z]$…

Let $R$ be a semilocal principal ideal domain. Two algebraic objects over $R$ in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all…

Let p be a prime and q=p^g. We show that the Grothendieck ring of finitely generated F_{q}[SL(2,F_{q})]-modules is naturally isomorphic to the quotient of the polynomial algebra Z[x] by the ideal generated by f^[g](x)-x, where…