17 citations · 37 across the 16 of their papers we have counts for
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Peter-Weyl theorem for Iwahori groups and highest weight categories
Evgeny Feigin, Anton Khoroshkin, Ievgen Makedonskyi +1
We study the algebra of functions on the Iwahori group via the category of graded bounded representations of its Lie algebra. In particular, we identify the standard and costandard…
Nonsymmetric -Cauchy identity and representations of the Iwahori algebra
Evgeny Feigin, Ievgen Makedonskyi, Daniel Orr
The specialization of the Mimachi-Noumi Cauchy-type identity rewrites certain infinite product in terms of specialized nonsymmetric Macdonald polynomials of type . We i…
Inverse -Chevalley formulas for semi-infinite flag manifolds, I: minuscule weights in ADE type
Takafumi Kouno, Satoshi Naito, Daniel Orr +1
We prove an explicit inverse Chevalley formula in the equivariant -theory of semi-infinite flag manifolds of simply-laced type. By an inverse Chevalley formula, we mean a formul…
Equivariant -theory of the semi-infinite flag manifold as a nil-DAHA module
Daniel Orr
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 (n…
Walk algebras, distinguished subexpressions, and point counting in Kac-Moody flag varieties
Dinakar Muthiah, Daniel Orr
We study walk algebras and Hecke algebras for Kac-Moody root systems. Each choice of orientation for the set of real roots gives rise to a corresponding "oriented" basis for each o…
On the double-affine Bruhat order: the conjecture and classification of covers in ADE type
Dinakar Muthiah, Daniel Orr
For any Kac-Moody group , we prove that the Bruhat order on the semidirect product of the Weyl group and the Tits cone for is strictly compatible with a $\…