We study Sp2n(R)-invariant functionals on the spaces of smooth vectors in Speh representations of GL2n(R). For even n we give expressions for such invariant functionals using an explicit realization of the space of smooth vectors in the Speh representations. Furthermore, we show that the functional we construct is, up to a constant, the unique functional on the Speh representation which is inva...

In this paper, we give an explicit formula of Chevalley type, in terms the Bruhat graph, for quantum multiplication with class line bundle associated to anti-dominant minuscule fundamental weight −ϖk torus-equivariant K-group partial flag manifold G/PJ (where J=I∖{k}) corresponding maximal (standard) parabolic subgroup PJ type A, D, E, or B. This result is obtained by proving a similar semi-inf...

• Generic algebras • Strict Iwahori-Hecke algebras • Representations with Iwahori-fixed vectors • Proof of the Borel-Matsumoto theorem • Irreducibility criteria Using the ideas of [Casselman 1980] descended from the Borel-Matsumoto theorem on admissible representations of p-adic reductive groups containing Iwahori-fixed vectors, it is possible to give an easily verifiable sufficient criterion f...

In this paper, for any simple, simply connected algebraic group G of type B n , C n or D n and for any maximal parabolic subgroup P of G, we describe all minimal dimensional Schubert varieties in G/P admitting semistable points for the action of a maximal torus T with respect to an ample line bundle on G/P. In this paper, we also describe, for any semi-simple simply connected algebraic group G ...

Let H and K be subgroups of a finite group G . Pick g ? uniformly at random. We study the distribution induced on double cosets. Three examples are treated in detail: 1) = Borel subgroup L n ( F q ) This leads to new theorems for Mallows measure permutations insights into LU matrix factorization. 2) The cosets hyperoctahedral inside S 2 , which applications Ewens's sampling formula mathematical...

Parabolic systems defined over GF(q) have been classified by Timmesfeld for q > 4 and by Stroth for q = 2 (see references). We deal with the case q = 3 . Parabolic systems have been classified by Niles, Timmesfeld, Stroth, and Heiss, if the field of definition is G F (2) or has at least four elements. [Ni, Timl, Tim2, Tim5, Tim7, Stl, St2, St3, He]. We treat the GF(3) case, where only partial r...

Let [Formula: see text] be a minimal parabolic subgroup of real reductive Lie group and closed text]. Then it is proved by Kobayashi Oshima that the regular representation contains each irreducible at most finitely many times if number text]-orbits on finite. Moreover, they also multiplicities are uniformly bounded finite, where complexifications text], respectively, Borel In this paper, we pro...

Over a field of positive characteristic, semisimple algebraic group G may have some nonreduced parabolic subgroup P. In this paper, we study the Schubert and Bott–Samelson–Demazure–Hansen (BSDH) varieties G/P, with P nonreduced, when base is perfect. It shown that, in general, BSDH such G/P are not normal, projection variety onto has fibers at closed points. When finite, generalized convolution...