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GKM-theoretical description of double coinvariant rings of pseudo-reflection groups
[The 5th Korea Toric Topology Winter Workshop]
Date: 2019-01-23
Speaker : Takashi Sato (Osaka City University)
Abstract : The double coinvariant ring of a pseudo-reflection group is a quotient ring of the tensor product of two copies of the ring of polynomial functions on the vector space on which the pseudo-reflection group acts. It is an analogue of the equivariant cohomology rings of flag varieties. There is a natural homomorphism from the double coinvariant ring to the direct product of copies of the ring of polynomial functions, and McDaniel shows that its image is described in terms of pseudo-reflections analogously to the GKM theory. I will introduce his work and give other description which is more suitable for combinatorics.
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