Notes on affine canonical and monomial bases

Details Notes on affine canonical and monomial bases Notes on affine canonical and monomial bases

2006-10-14

arxiv.org/abs/math/0610449v2

Mathematics

Representation Theory

24 pages. Title changed. The relation with Nakajima's conjecture clarified.

Scientific paper

We investigate the affine canonical basis and the monomial basis constructed in [LXZ] in Lusztig's geometric setting. We show that the transition matrix between the two bases is upper triangular with 1's in the diagonal and coefficients in the upper diagonal entries in N[v, v^{-1}]. As a consequence, we show that part of the monomial basis elements give rise to resolutions of support varieties of the affine canonical basis elements as simple perverse sheaves.

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