Degenerate flag varieties of type A: Frobenius splitting and BW theorem

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

Abstract

Let Fλa be the PBW degeneration of the flag varieties of type An-1. These varieties are singular and are acted upon with the degenerate Lie group SLna. We prove that Fλa have rational singularities, are normal and locally complete intersections, and construct a desingularization Rλ of Fλa. The varieties Rλ can be viewed as towers of successive ℙ1-fibrations, thus providing an analogue of the classical Bott-Samelson-Demazure-Hansen desingularization. We prove that the varieties Rλ are Frobenius split. This gives us Frobenius splitting for the degenerate flag varieties and allows to prove the Borel-Weil type theorem for Fλa. Using the Atiyah-Bott-Lefschetz formula for Rλ, we compute the q-characters of the highest weight sln-modules.

Original languageEnglish
Pages (from-to)55-77
Number of pages23
JournalMathematische Zeitschrift
Volume275
Issue number1-2
DOIs
Publication statusPublished - Oct 2013
Externally publishedYes

Fingerprint

Dive into the research topics of 'Degenerate flag varieties of type A: Frobenius splitting and BW theorem'. Together they form a unique fingerprint.

Cite this