Equivariant $K$-theory of the semi-infinite flag manifold as a nil-DAHA module
Abstract
The equivariant -theory of the semi-infinite flag manifold, as developed recently by Kato, Naito, and Sagaki, carries commuting actions of the nil-double affine Hecke algebra (nil-DAHA) and a -Heisenberg algebra. The action of the latter generates a free submodule of rank , where is the (finite) Weyl group. We show that this submodule is stable under the nil-DAHA, which enables one to express the nil-DAHA action in terms of matrices over the -Heisenberg algebra. Our main result gives an explicit algebraic construction of these matrices as a limit from the (non-nil) DAHA in simply-laced type. This construction reveals that multiplication by equivariant scalars, when expressed in terms of the Heisenberg algebra, is given by the nonsymmetric -Toda system introduced by Cherednik and the author.
Keywords
Cite
@article{arxiv.2001.03490,
title = {Equivariant $K$-theory of the semi-infinite flag manifold as a nil-DAHA module},
author = {Daniel Orr},
journal= {arXiv preprint arXiv:2001.03490},
year = {2020}
}