On The Poincare Series of Quadratic Algebras Associated to Hecke Symmetries

Hecke symmetries generalize the usual tensor symmetry of vector spaces $v\otimes w\text{arrow}w\otimes v$ as well as the symmetry of vector superspaces. To a Hecke symmetry $R$ there associates a quadratic algebra which can be interpreted as the function algebra upon a certain quantum space. This paper investigates the Poincare series of this quadratic algebra. We showthat it is a rational function with numerator and denominator being a reciprocal polynomial and a skew-reciprocal polynomial, respectively.