48 citations · 188 across the 28 of their papers we have counts for
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Affine PBW Bases and Affine MV polytopes
Dinakar Muthiah, Peter Tingley
We show how affine PBW bases can be used to construct affine MV polytopes, and that the resulting objects agree with the affine MV polytopes recently constructed using either prepr…
PBW bases and marginally large tableaux in type D
Ben Salisbury, Adam Schultze, Peter Tingley
We give an explicit description of the unique crystal isomorphism between two realizations of in type : that using marginally large tableaux and that using PBW monom…
Combinatorial descriptions of the crystal structure on certain PBW bases
Ben Salisbury, Adam Schultze, Peter Tingley
Using the theory of PBW bases, one can realize the crystal for any semisimple Lie algebra over using Kostant partitions as the underlying set. In fact ther…
Quiver varieties and crystals in symmetrizable type via modulated graphs
Vinoth Nandakumar, Peter Tingley
Kashiwara and Saito have a geometric construction of the infinity crystal for any symmetric Kac-Moody algebra. The underlying set consists of the irreducible components of Lusztig'…
Combinatorial descriptions of the crystal structure on certain PBW bases (extended abstract)
Ben Salisbury, Adam Schultze, Peter Tingley
Lusztig's theory of PBW bases gives a way to realize the infinity crystal for any simple complex Lie algebra where the underlying set consists of Kostant partitions. In fact, there…
Elementary construction of Lusztig's canonical basis
Peter Tingley
In this largely expository article we present an elementary construction of Lusztig's canonical basis in type ADE. The method, which is essentially Lusztig's original approach, is…