$q$-identities and affinized projective varieties, I. Quadratic monomial ideals

Details $q$-identities and affinized projective varieties, I. Quadratic monomial ideals $q$-identities and affinized projective varieties, I. Quadratic monomial ideals

1999-02-07

arxiv.org/abs/math-ph/9902010v1

Commun. Math. Phys. 210 (2000) 641-661

Physics

Mathematical Physics

AMSTeX, 22 pages

Scientific paper

10.1007/s002200050794

We define the concept of an affinized projective variety and show how one can, in principle, obtain q-identities by different ways of computing the Hilbert series of such a variety. We carry out this program for projective varieties associated to quadratic monomial ideals. The resulting identities have applications in describing systems of quasi-particles containing null-states and can be interpreted as alternating sums of quasi-particle Fock space characters.

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