On the relation of Clifford-Lipschitz groups to q-symmetric groups
Abstract
Description
It can be shown that it is possible to find a representation of Hecke algebras within Clifford algebras of multivectors. These Clifford algebras possess a unique gradation and a possibly non-symmetric bilinear form. Hecke algebra representations can be classified, for non-generic q, by Young tableaux of the symmetric group due to the isomorphy of the group algebras for q ->1. Since spinors can be constructed as elements of minimal left (right) ideals obtained by the left (right) action on primitive idempotents, we are able to construct q-spinors from q-Young operators corresponding to the appropriate symmetry type. It turns out that an anti-symmetric part in the Clifford bilinear form is necessary. q-deformed reflections (Hecke generators) can be obtained only for even multivector aggregates rendering this symmetry a composite one. In this construction one is able to deform spin groups only, though not pin groups. The method is closely related to a projective interpretation.
5 pages LaTeX, uses icmp.sty; Contribution to the XXII Int. Colloquium on Grp. Theor. Meth. in Phys. 13.--18. July 1998 in HOBART, Tasmania / Austarlia; (Bertfried.Fauser@uni-konstanz.de)
5 pages LaTeX, uses icmp.sty; Contribution to the XXII Int. Colloquium on Grp. Theor. Meth. in Phys. 13.--18. July 1998 in HOBART, Tasmania / Austarlia; (Bertfried.Fauser@uni-konstanz.de)