49 citations · 658 across the 61 of their papers we have counts for
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The quantum isomeric supercategory
Alistair Savage
We introduce the quantum isomeric supercategory and the quantum affine isomeric supercategory. These diagrammatically defined supercategories, which can be viewed as isomeric analo…
Quantum diagrammatics for
Alistair Savage, Bruce W. Westbury
We introduce a graphical calculus for the representation theory of the quantized enveloping algebra of type . We do this by giving a diagrammatic description of the category o…
Categorification of the elliptic Hall algebra
Youssef Mousaaid, Alistair Savage
We show that the central charge reduction of the universal central extension of the elliptic Hall algebra is isomorphic to the trace, or zeroth Hochschild homology, of the quan…
Quantum affine wreath algebras
Daniele Rosso, Alistair Savage
To each symmetric algebra we associate a family of algebras that we call quantum affine wreath algebras. These can be viewed both as symmetric algebra deformations of affine Hecke…
Twisted Heisenberg doubles
Daniele Rosso, Alistair Savage
We introduce a twisted version of the Heisenberg double, constructed from a twisted Hopf algebra and a twisted Hopf pairing. We state a Stone--von Neumann type theorem for a natura…
Braided and coboundary monoidal categories
Alistair Savage
In this expository paper, we discuss and compare the notions of braided and coboundary monoidal categories. Coboundary monoidal categories are analogues of braided monoidal categor…
Crystals, quiver varieties and coboundary categories for Kac-Moody algebras
Alistair Savage
Henriques and Kamnitzer have defined a commutor for the category of crystals of a finite-dimensional complex reductive Lie algebra that gives it the structure of a coboundary categ…
Geometric and Combinatorial Realizations of Crystals of Enveloping Algebras
Alistair Savage
Kashiwara and Saito have defined a crystal structure on the set of irreducible components of Lusztig's quiver varieties. This gives a geometric realization of the crystal graph of…
A geometric construction of crystal graphs using quiver varieties: Extension to the non-simply laced case
Alistair Savage
We consider a generalization of the quiver varieties of Lusztig and Nakajima to the case of all symmetrizable Kac-Moody Lie algebras. To deal with the non-simply laced case one con…
Quiver varieties and fusion products for sl_2
Alistair Savage, Olivier Schiffmann
We construct the fusion product of finite-dimensional sl_2-modules in the homology of (or in the space of constructible functions on) a certain subvariety L_l(w_1, ..., w_r) of Nak…