Let S be a single condition Schubert variety with an arbitrary number of strata. Recently, an explicit description of the summands involved in the decomposition theorem applied to such a variety has been obtained in a paper of the second author. Starting from this result, we provide an explicit description of the Poincaré polynomial of the intersection cohomology of S by means of the Poincaré polynomials of its strata, obtaining interesting polynomial identities relating Poincaré polynomials of several Grassmannians, both by a local and by a global point of view. We also present a symbolic study of a particular case of these identities.
Polynomial identities related to special Schubert varieties / Cioffi, F.; Franco, D.; Sessa, C.. - In: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING. - ISSN 0938-1279. - 34:2(2023), pp. 245-265. [10.1007/s00200-021-00496-6]
Polynomial identities related to special Schubert varieties
Cioffi F.
;Franco D.;Sessa C.
2023
Abstract
Let S be a single condition Schubert variety with an arbitrary number of strata. Recently, an explicit description of the summands involved in the decomposition theorem applied to such a variety has been obtained in a paper of the second author. Starting from this result, we provide an explicit description of the Poincaré polynomial of the intersection cohomology of S by means of the Poincaré polynomials of its strata, obtaining interesting polynomial identities relating Poincaré polynomials of several Grassmannians, both by a local and by a global point of view. We also present a symbolic study of a particular case of these identities.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.