Abstract
Using the theory of Schur functions, we prove that the coefficients of the Hilbert series of a quadraticR-matrix algebra (for a Heckian R-matrix) form a totally positive sequence. The well-known description of the generation series for totally positive sequences implies that the Hilbert series of the quadratic R-matrix algebra is rational with real positive poles and real negative zeros. Using this characterization, we obtain the examples of Koszul and non-R-matrix algebras.
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