Alternating Formulas for K-theoretic Quiver Polynomials
نویسنده
چکیده
The main theorem here is the K-theoretic analogue of the cohomological ‘stable double component formula’ for quiver polynomials in [KMS03]. This K-theoretic version is still in terms of lacing diagrams, but nonminimal diagrams contribute terms of higher degree. The motivating consequence is a conjecture of Buch on the sign-alternation of the coefficients appearing in his expansion of quiver K-polynomials in terms of stable Grothendieck polynomials for partitions [Buc02a].
منابع مشابه
GROTHENDIECK POLYNOMIALS AND QUIVER FORMULAS By ANDERS S. BUCH, ANDREW KRESCH, HARRY TAMVAKIS, and ALEXANDER YONG
Fulton’s universal Schubert polynomials give cohomology formulas for a class of degeneracy loci, which generalize Schubert varieties. The K-theoretic quiver formula of Buch expresses the structure sheaves of these loci as integral linear combinations of products of stable Grothendieck polynomials. We prove an explicit combinatorial formula for the coefficients, which shows that they have altern...
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