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108 - Ryosuke Kodera 2015
The localized equivariant homology of the quiver variety of type $A_{N-1}^{(1)}$ can be identified with the level one Fock space by assigning a normalized torus fixed point basis to certain symmetric functions, Jack($mathfrak{gl}_N$) symmetric functi ons introduced by Uglov. We show that this correspondence is compatible with actions of two algebras, the Yangian for $mathfrak{sl}_N$ and the affine Lie algebra $hat{mathfrak{sl}}_N$, on both sides. Consequently we obtain affine Yangian action on the Fock space.
117 - Ryosuke Kodera 2009
We calculate the first extension groups for finite-dimensional simple modules over an arbitrary generalized current Lie algebra, which includes the case of loop Lie algebras and their multivariable analogs.
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