A HOMOLOGICAL STUDY OF GREEN POLYNOMIALS

作者：Kato Syu^*

来源：Annales Scientifiques de l'Ecole Normale Superieure, 2015, 48(5): 1035-1074.

DOI：10.24033/asens.2265

We interpret the orthogonality relation of Kostka polynomials arising from complex reflection groups ([51, 52] and [35]) in terms of homological algebra. This leads us to the notion of Kostka system, which can be seen as a categorical counterpart of Kostka polynomials. Then, we show that every generalized Springer correspondence ([34]) in a good characteristic gives rise to a Kostka system. This enables us to see the top-term generation property of the (twisted) homology of generalized Springer fibers, and the transition formula of Kostka polynomials between two generalized Springer correspondences of type BC. The latter provides an inductive algorithm to compute Kostka polynomials by upgrading [16]3 to its graded version. In the appendices, we present purely algebraic proofs that Kostka systems exist for type A and asymptotic type BC cases, and therefore one can skip geometric sections 3-5 to see the key ideas and basic examples/techniques.

• 出版日期2015-10