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Double-affine Kazhdan-Lusztig polynomials via masures
Dinakar Muthiah
Masures (previously also known as hovels) are a generalization of the theory of affine buildings for arbitrary -adic Kac-Moody groups. Gaussent and Rousseau invented masures to…
Symplectic leaves for generalized affine Grassmannian slices
Dinakar Muthiah, Alex Weekes
The generalized affine Grassmannian slices are algebraic varieties introduced by Braverman, Finkelberg, and Nakajima in their study of Coulomb branches…
Weyl group action on weight zero Mirković-Vilonen basis and equivariant multiplicities
Dinakar Muthiah
We state a conjecture about the Weyl group action coming from Geometric Satake on zero-weight spaces in terms of equivariant multiplicities of Mirković-Vilonen cycles. We prove it…
Correction factors for Kac-Moody groups and -deformed root multiplicities
Dinakar Muthiah, Anna Puskás, Ian Whitehead
We study a correction factor for Kac-Moody root systems which arises in the theory of -adic Kac-Moody groups. In affine type, this factor is known, and its explicit computation…
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 a reducedness conjecture for spherical Schubert varieties and slices in the affine Grassmannian
Joel Kamnitzer, Dinakar Muthiah, Alex Weekes
We study spherical Schubert varieties in the affine Grassmannian. These Schubert varieties have a natural conjectural modular description due to Finkelberg-Mirković. This modular d…