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- W2952597853 abstract "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 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." @default.
- W2952597853 created "2019-06-27" @default.
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- W2952597853 date "2011-03-08" @default.
- W2952597853 modified "2023-09-27" @default.
- W2952597853 title "Degenerate flag varieties of type A: Frobenius splitting and BW theorem" @default.
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