Localization for quantum groups at a root of unity by Backelin, E, Kremnizer, K

The Haagerup property for locally compact quantum groups by Daws, M, Fima, P, Skalski, A, White, S

“…We use these characterisations to show that the Haagerup property is preserved under free products of discrete quantum groups.…”

Singular localization for Quantum groups at generic $q$ by Backelin, E, Kremnizer, K

Langlands duality for representations and quantum groups at a root of unity by McGerty, K

“…We give a representation-theoretic interpretation of the Langlands character duality of Frenkel and Hernandez, and show that the "Langlands branching multiplicities" for symmetrizable Kac-Moody Lie algebras are equal to certain tensor product multiplicities. For finite type quantum groups, the connection with tensor products can be explained in terms of tilting modules.…”

Bilinear forms, Clifford algebras, $q$-commutation relations, and quantum groups by Hannabuss, K

“…Constructions are described which associate algebras to arbitrary bilinear forms, generalising the usual Clifford and Heisenberg algebras. Quantum groups of symmetries are discussed, both as deformed enveloping algebras and as quantised function spaces. …”

Quantum flag varieties, equivariant quantum D-modules and localization of quantum groups by Backelin, E, Kremnizer, K

A quantum Witt construction by Hannabuss, K

“…This construction generalises a standard construction of quantum groups, and also supergroups, but it also provides alternative constructions for some quantum groups, including the quantum exceptional group <em>e</em>₈. © 1998 Academic Press.…”

Hall algebras and the Quantum Frobenius by McGerty, K

“…Lusztig has constructed a Frobenius morphism for quantum groups at an $\ell$-th root of unity, which gives an integral lift of the Frobenius map on universal enveloping algebras in positive characteristic. …”

Highest weights, projective geometry, and the classical limit: I. Geometrical aspects and the classical limit by Hannabuss, K

“…Various generalisations to Clifford algebras and quantum groups are explored, as well as the relationship between geometry, second quantisation, and the classical limit. © 2000 Elsevier Science B.V.…”

Global quantum differential operators on quantum flag manifolds, theorems of Duflo and Kostant by Backelin, E, Kremnizer, K

“…We also describe the center of the ad-integrable part of the quantum group and the adjoint Lie algebra action on it.…”

The Kronecker quiver and bases of quantum affine sl_2 by McGerty, K

“…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.…”

Integrability and braided tensor categories by Fendley, P

“…Such currents have been constructed by utilising quantum-group algebras and ideas from “discrete holomorphicity”. …”

On the geometric realization of the inner product and canonical basis for quantum affine $\mathfrak{sl}_n$ by McGerty, K

“…We give a geometric interpretation of the inner product on the modified quantum group of $\hat{\mathfrak{sl}}_n$. We also give some applications of this interpretation, including a positivity result for the inner product, and a new geometric construction of the canonical basis.…”

Cells in quantum affine sl_n by McGerty, K

“…Using the geometric construction of the quantum group due to Lusztig and Ginzburg--Vasserot, we describe explicitly the two-sided cells, the number of left cells in a two--sided cell, and the asymptotic algebra, verifying conjectures of Lusztig.…”

Onsager symmetries in $U(1)$ -invariant clock models by Vernier, E, O'Brien, E, Fendley, P

“…We construct the elements of the algebra explicitly from transfer matrices built from non-fundamental representations of the quantum-group algebra . We analyse the spectra further by using both the coordinate Bethe ansatz and a functional approach, and show that the degeneracies result from special exact n-string solutions of the Bethe equations. …”

Modified Turaev-Viro invariants from quantum 𝔰𝔩(2|1) by Anghel, CA, Geer, N

“…Loosely speaking, the standard way to obtain such a category from a quantum group is: (1) specialize q to a root of unity; this forces some modules to have zero quantum dimension, (2) quotient by morphisms of modules with zero quantum dimension, (3) show the resulting category is finite and semi-simple. …”