Poincaré Series of Quantum Spaces Associated to Hecke Operators

Details Poincaré Series of Quantum Spaces Associated to Hecke Operators Poincaré Series of Quantum Spaces Associated to Hecke Operators

1997-11-23

arxiv.org/abs/q-alg/9711020v1

Acta Math. Vietnamica, 24:2(1999), 235-246

Mathematics

Quantum Algebra

latex 2.09, amsart style, 8 pages

Scientific paper

We study the Poincar\'e series of the quantum spaces associated to a Hecke operator, i.e., a Yang-Baxter operator satisfying the equation $(x+1)(x-q)=0$. The Poincar\'e series of the corresponding matrix bialgebra is also considered. Using an old result on Poly\'a frequency sequence, we show that the Poincar\'e series of quantum spaces are always rational functions having negative roots and positive poles. In particular, we show that the rank of an even Hecke operator should be rational functions having negative roots and positive poles. In particular, we show that the rank of an even Hecke operator should be greater than the dimension of the vector space it is acting on.

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