Frobenius character formula and spin generic degrees for Hecke-Clifford algebra

The spin analogues of several classical concepts and results for Hecke algebras are established. A Frobenius type formula is obtained for irreducible characters of the Hecke-Clifford algebra. A precise characterization of the trace functions allows us to define the character table for the algebra. The algebra is endowed with a canonical symmetrizing trace form, with respect to which the spin generic degrees are formulated and shown to coincide with the spin fake degrees. We further provide a characterization of the trace functions and the symmetrizing trace form on the spin Hecke algebra which is Morita super-equivalent to the Hecke-Clifford algebra.