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

Details Degenerate flag varieties of type A: Frobenius splitting and BWB theorem Degenerate flag varieties of type A: Frobenius splitting and BWB theorem

2011-03-08

arxiv.org/abs/1103.1491v3

Mathematics

Algebraic Geometry

26 pages

Scientific paper

Let $\Fl^a_\la$ be the PBW degeneration of the flag varieties of type $A_{n-1}$. These varieties are singular and are acted upon with the degenerate Lie group $SL_n^a$. We prove that $\Fl^a_\la$ have rational singularities, are normal and locally complete intersections, and construct a desingularization $R_\la$ of $\Fl^a_\la$. The varieties $R_\la$ can be viewed as towers of successive $\bP^1$-fibrations, thus providing an analogue of the classical Bott-Samelson-Demazure-Hansen desingularization. We prove that the varieties $R_\la$ are Frobenius split. This gives us Frobenius splitting for the degenerate flag varieties and allows to prove the Borel-Weyl-Bott type theorem for $\Fl^a_\la$. Using the Atiyah-Bott-Lefschetz formula for $R_\la$, we compute the $q$-characters of the highest weight $\msl_n$-modules.

Affiliated with

Also associated with

No associations

Rating

Degenerate flag varieties of type A: Frobenius splitting and BWB theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Degenerate flag varieties of type A: Frobenius splitting and BWB theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Degenerate flag varieties of type A: Frobenius splitting and BWB theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-82404