5 research outputs found

    Hecke algebras of finite type are cellular

    Full text link
    Let \cH be the one-parameter Hecke algebra associated to a finite Weyl group WW, defined over a ground ring in which ``bad'' primes for WW are invertible. Using deep properties of the Kazhdan--Lusztig basis of \cH and Lusztig's \ba-function, we show that \cH has a natural cellular structure in the sense of Graham and Lehrer. Thus, we obtain a general theory of ``Specht modules'' for Hecke algebras of finite type. Previously, a general cellular structure was only known to exist in types AnA_n and BnB_n.Comment: 14 pages; added reference

    A class of Calogero type reductions of free motion on a simple Lie group

    Full text link
    The reductions of the free geodesic motion on a non-compact simple Lie group G based on the G+×G+G_+ \times G_+ symmetry given by left- and right multiplications for a maximal compact subgroup G+⊂GG_+ \subset G are investigated. At generic values of the momentum map this leads to (new) spin Calogero type models. At some special values the `spin' degrees of freedom are absent and we obtain the standard BCnBC_n Sutherland model with three independent coupling constants from SU(n+1,n) and from SU(n,n). This generalization of the Olshanetsky-Perelomov derivation of the BCnBC_n model with two independent coupling constants from the geodesics on G/G+G/G_+ with G=SU(n+1,n) relies on fixing the right-handed momentum to a non-zero character of G+G_+. The reductions considered permit further generalizations and work at the quantized level, too, for non-compact as well as for compact G.Comment: shortened to 13 pages in v2 on request of Lett. Math. Phys. and corrected some spelling error

    III. ABTEILUNG

    No full text
    corecore