38 citations · 72 across the 16 of their papers we have counts for
6 papers · 1 filter
On the geometric realization of the inner product and canonical basis for quantum affine
Kevin McGerty
We give a geometric interpretation of the inner product on the modified quantum group of . We also give some applications of this interpretation, including a…
Langlands duality for representations and quantum groups at a root of unity
Kevin McGerty
We give a representation-theoretic interpretation of the Langlands character duality of Frenkel and Hernandez, and show that the "Langlands branching multiplicities" for symmetriza…
Hall algebras and the Quantum Frobenius
Kevin McGerty
Lusztig has constructed a Frobenius morphism for quantum groups at an -th root of unity, which gives an integral lift of the Frobenius map on universal enveloping algebras in…
q-Schur algebras and quantum Frobenius
Kevin McGerty
The quantum Frobenius map and it splitting are shown to descend to corresponding maps for generalized -Schur algebras at a root of unity. We also define analogs of -Schur alg…
The Kronecker quiver and bases of quantum affine sl_2
Kevin McGerty
We compare various bases of the affine quantum group $\mathbfU^ (\hat\mathfrak{sl}_2)$ in the context of the Kronecker quiver, and relate them to the Drinfeld presentation.
Cells in quantum affine sl_n
Kevin McGerty
We study Lusztig's theory of cells for quantum affine . Using the geometric construction of the quantum group due to Lusztig and Ginzburg--Vasserot, we describe ex…