On Theta Pairs for a Maximal Subgroup

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...

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

Intertwining Operators for Representations Induced from a Maximal Parabolic Subgroup

We present a new method of calculating intertwining operators between principal series representations of semisimple Lie groups G. Working in the compact realization we nd the eigenvalues of the operators on the K-types, and give several examples. Among the advantages of our method is its applicability to bundle-valued cases. 0. Introduction Intertwining operators of various forms play an impor...

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

Theta Lifting of Nilpotent Orbits for Symmetric Pairs

We consider a reductive dual pair (G,G′) in the stable range with G′ the smaller member and of Hermitian symmetric type. We study the theta lifting of nilpotent K ′ C-orbits, where K ′ is a maximal compact subgroup of G′ and we describe the precise KC-module structure of the regular function ring of the closure of the lifted nilpotent orbit of the symmetric pair (G,K). As an application, we pro...