Related papers: Bounded reduction for Chevalley groups of types $E…

We examine certain maps from root systems to vector spaces over finite fields. By choosing appropriate bases, the images of these maps can turn out to have nice combinatorial properties, which reflect the structure of the underlying root…

We prove a decomposition of definable groups in o-minimal structures generalizing the Jordan-Chevalley decomposition of linear algebraic groups. It follows that any definable linear group G is a semidirect product of its maximal normal…

We prove a reduced version of the Chevalley restriction conjecture on the commuting scheme posed by T.H. Chen and B.C. Ng\^o, extending the results of Hunziker for classical groups. In particular, we prove that for any connected reductive…

For any simple complex Lie algebra $\mathfrak{g}$, we show that the degrees of the "ADO" link polynomials coming from the unrolled restricted quantum group $\overline{U}^H_q(\mathfrak{g})$ at a root of unity give lower bounds to the Seifert…

Chevalley group schemes are group schemes defined over the integers that parametrize connected reductive groups over algebraically closed fields as geometric fibers. In this paper, we construct closed subgroup schemes of Chevalley group…

Polynomial functions on the group of units Q_n of the ring Z_{2^n} are considered. A finite set of reduced polynomials RP_n in Z[x] that induces the polynomial functions on Q_n is determined. Each polynomial function on Q_n is induced by a…

The classification of equivariant toroidal embeddings of a reductive group over an algebraically closed field is combinatorial and does not depend on the characteristic of the base field. This suggests that there should exist ``universal''…

Let $P(\partial_0,\partial_1,...,\partial_n)$ be a PDO on $\symR^{1+n}$ with constant coefficients. It is proved that (i) the real parts of the $\lambda$-roots of the polynomial $P(\lambda,i\xi_1,...,i\xi_n)$ are bounded from above when…

We show that the standard set of elementary generators of an elementary isotropic reductive group over a connected finitely generated ring is a Kazhdan subset. This generalizes the corresponding result of M. Ershov, A. Jaikin-Zapirain, and…

Chevalley's theorem states that for any simple finite dimensional Lie algebra G (1) the restriction homomorphism of the algebra of polynomials on G onto the Cartan subalgebra H induces an isomorphism between the algebra of G-invariant…

Let (g,k) be a reductive symmetric superpair of even type, i.e. so that there exists an even Cartan subspace a in p. The restriction map S(p^*)^k->S(a^*)^W where W=W(g_0:a) is the Weyl group, is injective. We determine its image explicitly.…

We prove part of a higher rank analogue of the Mazur-Gouvea Conjecture. More precisely, let $\tilde{\bf G}$ be a connected, reductive ${\Bbb Q}$-split group and let $\Gamma$ be an arithmetic subgroup of $\tilde{\bf G}$. We show that the…

Given a universal elementary Chevalley-Demazure group $E_\Phi^{sc}(R)$ for which its (standard) parabolic subgroups are finitely generated, we consider the problem of classifying which parabolics $P(R) \subset E_\Phi^{sc}(R)$ are finitely…

Let $V$ be a finite-dimensional vector space over a finite field, and suppose $G \leq \Gamma \mathrm{L}(V)$ is a group with a unique subnormal quasisimple subgroup $E(G)$ that is absolutely irreducible on $V$. A base for $G$ is a set of…

We describe the equivariant Chow ring of the wonderful compactification $X$ of a symmetric space of minimal rank, via restriction to the associated toric variety $Y$. Also, we show that the restrictions to $Y$ of the tangent bundle $T_X$…

We find a new representation of the simple Lie algebra of type $E_7$ on the polynomial algebra in 27 variables, which gives a fractional representation of the corresponding Lie group on 27-dimensional space. Using this representation and…

We study the moduli stack of degree $0$ semistable $G$-bundles on an irreducible curve $E$ of arithmetic genus $1$, where $G$ is a connected reductive group. Our main result describes a partition of this stack indexed by a certain family of…

A ring $R$ is an elementary divisor ring if every matrix over $R$ admits a diagonal reduction. We further explore various stable like conditions on a bezout duo-domain under which it is an elementary divisor domain. Many known results are…

This paper gives an explicit argument to show strong boundedness for ${\rm Sp}_{2n}(R)$ for $R$ a ring of S-algebraic integers or a semi-local ring. This gives a quantitative version of a related abstract result in a previous paper of the…

The paper studies lower bounds for the dimensions of projective indecomposable modules for Chevalley groups G in defining characteristic p. The main result extending earlier one by Malle and Weigel (2008) determines the modules in question…