30 citations · 87 across the 9 of their papers we have counts for
10 papers
Canonical bases for the quantum enveloping algebra of gl(m|1) and its modules
Sean Clark
We construct a crystal basis for the negative half of the quantum group U associated to the standard super Cartan datum of gl(m|1), which is compatible with known crystals on Kac m…
Quantum osp(1|2n) knot invariants are the same as quantum so(2n+1) knot invariants
Sean Clark
We show that the quantum covering group associated to osp(1|2n) has an associated colored quantum knot invariant à la Reshetikhin-Turaev, which specializes to a quantum knot invari…
Quantum supergroups V. Braid group action
Sean Clark, David Hill
We construct a braid group action on quantum covering groups. We further use this action to construct a PBW basis for the positive half in finite type which is pairwise-orthogonal…
Quantum supergroups IV. The modified form
Sean Clark
We construct a canonical basis for a class of tensor product modules of a quantum covering group associated to a Kac-Moody Lie superalgebra of anisotropic type, and use these bases…
Quantum Shuffles and Quantum Supergroups of Basic Type
Sean Clark, David Hill, Weiqiang Wang
We initiate the study of several distinguished bases for the positive half of a quantum supergroup associated to a general super Cartan datum of…
Quantum Supergroups III. Twistors
Sean Clark, Zhaobing Fan, Yiqiang Li +1
We establish direct connections at several levels between quantum groups and supergroups associated to bar-consistent super Cartan datum by constructing an automorphism (called twi…
Quantum supergroups II. Canonical basis
Sean Clark, David Hill, Weiqiang Wang
Following Kashiwara's algebraic approach, we construct crystal bases and canonical bases for quantum supergroups with no isotropic odd roots and for their integrable modules.
Quantum Supergroups I. Foundations
Sean Clark, David Hill, Weiqiang Wang
In this part one of a series of papers, we introduce a new version of quantum covering and super groups with no isotropic odd simple root, which is suitable for the studies of inte…
Super tableaux and a branching rule for the general linear Lie superalgebra
Sean Clark, Yung-Ning Peng, Sittipong Thamrongpairoj
In this note, we formulate and prove branching rules of simple polynomial modules for the Lie superalgebra . Our branching rules depend on the conjugacy class o…
Canonical basis for quantum osp(1|2)
Sean Clark, Weiqiang Wang
We introduce a modified quantum enveloping algebra as well as a (modified) covering quantum algebra for the ortho-symplectic Lie superalgebra osp(1|2). Then we formulate and comput…