Invariant polynomials under the maximal unipotent subgroup of a classical group

On the Fischer-Clifford matrices of a maximal subgroup of the Lyons group Ly

The non-split extension group $overline{G} = 5^3{^.}L(3,5)$ is a subgroup of order 46500000 and of index 1113229656 in Ly. The group $overline{G}$ in turn has L(3,5) and $5^2{:}2.A_5$ as inertia factors. The group $5^2{:}2.A_5$ is of order 3 000 and is of index 124 in L(3,5). The aim of this paper is to compute the Fischer-Clifford matrices of $overline{G}$, which together with associated parti...

Actions of the Derived Group of a Maximal Unipotent Subgroup on G-varieties

The ground field k is algebraically closed and of characteristic zero. Let G be a semisimple simply-connected algebraic group over k and U a maximal unipotent subgroup of G. One of the fundamental invariant-theoretic facts, which goes back to Hadžiev [9], is that k[G/U ] is a finitely generated k-algebra and regarded as G-module it contains every finite-dimensional simple G-module exactly once....

Characterizing the Multiplicative Group of a Real Closed Field in Terms of its Divisible Maximal Subgroup

Quotients by Reductive Group, Borel Subgroup, Unipotent Group and Maximal Torus

Consider an algebraic action of a connected complex reductive algebraic group on a complex polarized projective variety. In this paper, we first introduce the nilpotent quotient, the quotient of the polarized projective variety by a maximal unipotent subgroup. Then, we introduce and investigate three induced actions: one by the reductive group, one by a Borel subgroup, and one by a maximal toru...

On a maximal subgroup of the Thompson simple group∗

The present paper deals with a maximal subgroup of the Thompson group, namely the group 2 + A9 := G. We compute its conjugacy classes using the coset analysis method, its inertia factor groups and Fischer matrices, which are required for the computations of the character table of G by means of Clifford-Fischer Theory. AMS subject classifications: 20C15, 20C40