15 research outputs found
Crystal energy functions via the charge in types A and C
The Ram-Yip formula for Macdonald polynomials (at t=0) provides a statistic
which we call charge. In types A and C it can be defined on tensor products of
Kashiwara-Nakashima single column crystals. In this paper we prove that the
charge is equal to the (negative of the) energy function on affine crystals.
The algorithm for computing charge is much simpler and can be more efficiently
computed than the recursive definition of energy in terms of the combinatorial
R-matrix.Comment: 25 pages; 1 figur
Standard Monomial Theory for desingularized Richardson varieties in the flag variety GL(n)/B
We consider a desingularization Gamma of a Richardson variety X_w^v=X_w \cap
X^v in the flag variety Fl(n)=GL(n)/B, obtained as a fibre of a projection from
a certain Bott-Samelson variety Z. We then construct a basis of the homogeneous
coordinate ring of Gamma inside Z, indexed by combinatorial objects which we
call w_0-standard tableaux
Notes on the geometric Satake equivalence
International audienceThese notes are devoted to a detailed exposition of the proof of the Geometric Satake Equivalence for general coefficients, following Mirkovic-Vilonen