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A bar operation on the double affine Hecke algebra
Dougal Davis, Ivan Losev, Calder Morton-Ferguson
We construct a bar-type operation for the affine Hecke algebra $\Ha$ attached to a symmetrizable Kac--Moody group. Our main tool is a geometric bimodule defined using the equivaria…
Weight modules and gluing of sheaves on the flag variety
Pablo Boixeda Alvarez, Calder Morton-Ferguson
We study a natural enlargement of the BGG Category O for a semisimple Lie algebra: the category of weight modules with trivial central character and finite-dimensional weight space…
Modular reduction of complex representations of finite reductive groups
Roman Bezrukavnikov, Michael Finkelberg, David Kazhdan +1
The main result describes the Brauer-Nesbitt reduction of unipotent representations of a finite group of Lie type, expressing it as an explicit linear combination of the restrictio…
Perverse sheaves and t-structures on the thin and thick affine flag varieties
Roman Bezrukavnikov, Calder Morton-Ferguson
We study the categories and of Iwahori-equivariant perverse sheaves on the thin and thick affine flag varieties ass…
Polishchuk's conjecture and Kazhdan-Laumon representations
Calder Morton-Ferguson
In their 1988 paper "Gluing of perverse sheaves and discrete series representations," D. Kazhdan and G. Laumon constructed an abelian category associated to a reducti…
Symplectic Fourier-Deligne transforms on G/U and the algebra of braids and ties
Calder Morton-Ferguson
We explicitly identify the algebra generated by symplectic Fourier-Deligne transforms (i.e. convolution with Kazhdan-Laumon sheaves) acting on the Grothendieck group of perverse sh…
Kazhdan-Laumon Category O, Braverman-Kazhdan Schwartz space, and the semi-infinite flag variety
Calder Morton-Ferguson
We define and study an analogue of Category O in the context of Kazhdan and Laumon's gluing construction for perverse sheaves on the basic affine space. We explicitly describe the…
Heaps, crystals, and preprojective algebra modules
Anne Dranowski, Balazs Elek, Joel Kamnitzer +1
Fix a simply-laced semisimple Lie algebra. We study the crystal , were is a dominant minuscule weight and is a natural number. On one hand, can be realized…