Related papers: Invariants in divided power algebras

The density property for a Stein manifold X implies that the group of holomorphic diffeomorphisms of X is infinite-dimensional and, in a certain well-defined sense, as large as possible. We prove that if G is a complex semisimple Lie group…

The classical theorem of Weitzenboeck states that the algebra of invariants of a single unipotent transformation $g$ in $GL_m(K)$ acting on the polynomial algebra $K[x_1,...,x_m]$ over a field $K$ of characteristic 0 is finitely generated.…

Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring over a field and $A$ a standard graded $S$-algebra. In terms of the Gr\"obner basis of the defining ideal $J$ of $A$ we give a condition, called the x-condition, which implies that all graded…

Leibniz algebras are certain generalizations of Lie algebras. Motivated by the concept of subinvariance in group theory, Schenkman studied properties of subinvariant subalgebras of a Lie algebra. In this paper we define subinvariant…

By now, we have a product theorem in every finite simple group $G$ of Lie type, with the strength of the bound depending only in the rank of $G$. Such theorems have numerous consequences: bounds on the diameters of Cayley graphs, spectral…

We study general nilpotent algebras. The results obtained are new even for the classical algebras, such as associative or Lie algebras. We single out certain generic properties of finite-dimensional algebras, mostly over infinite fields.…

We construct explicit formulae for the eigenvalues of certain invariants of the Lie superalgebra gl(m|n) using characteristic identities. We discuss how such eigenvalues are related to reduced Wigner coefficients and the reduced matrix…

We conjecture closed-form expressions for the Macdonald limits of the superconformal indices of the (A_1, A_{2n-3}) and (A_1, D_{2n}) Argyres-Douglas (AD) theories in terms of certain simple deformations of Macdonald polynomials. As checks…

Let $U$ be a unipotent group which is graded in the sense that it has an extension $H$ by the multiplicative group of the complex numbers such that all the weights of the adjoint action on the Lie algebra of $U$ are strictly positive. We…

This paper considers a finite group $G$ acting linearly on the variables $V$ of a polynomial algebra, or an exterior algebra, or superpolynomial algebra with both commuting and anticommuting variables. In this setting, the Hilbert series…

We show how to compute a certain group of equivalence classes of invariant Drinfeld twists on the algebra of a finite group G over a field k of characteristic zero. This group is naturally isomorphic to the second lazy cohomology group of…

In [2], the authors prove Stillman's conjecture in all characteristics and all degrees by showing that, independent of the algebraically closed field $K$ or the number of variables, $n$ forms of degree at most $d$ in a polynomial ring $R$…

Let G be a connected semisimple algebraic group over $k$, with Lie algebra $\g$. Let $\h$ be a subalgebra of $\g$. A simple finite-dimensional $\g$-module V is said to be $\h$-indecomposable if it cannot be written as a direct sum of two…

A $p$-divisible group over a field $K$ admits a slope decomposition; associated to each slope $\lambda$ is an integer $m$ and a representation $\gal(K) \ra \gl_m(D_\lambda)$, where $D_\lambda$ is the $\rat_p$-division algebra with Brauer…

A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…

When we consider the action of a finite group on a polynomial ring, a polynomial unchanged by the action is called an invariant polynomial. A famous result of Noether states that in characteristic zero the maximal degree of a minimal…

Let $X$ be an affine algebraic variety with a transitive action of the algebraic automorphism group. Suppose that $X$ is equipped with several non-degenerate fixed point free $SL_2$-actions satisfying some mild additional assumption. Then…

This paper studies generic and perturbation properties inside the linear space of $m\times (m+n)$ polynomial matrices whose rows have degrees bounded by a given list $d_1, \ldots, d_m$ of natural numbers, which in the particular case $d_1 =…

For modular Lie superalgebras, new notions are introduced: Divided power homology and divided power cohomology. For illustration, we give presentations (in terms of analogs of Chevalley generators) of finite dimensional Lie (super)algebras…

In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…