Positive Representations of Split Real Quantum Groups and Future Perspectives

DOI10.1093/imrn/rns288zbMath1381.17009arXiv1111.1033OpenAlexW2963350066MaRDI QIDQ3448320

Ivan Chi-Ho Ip, Igor B. Frenkel

Publication date: 23 October 2015

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.1033

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items (13)

Cluster realization of \(\mathcal{U}_q(\mathfrak{g})\) and factorizations of the universal \(R\)-matrix ⋮ On tensor product decomposition of positive representations of \(\mathcal{U}_{q\widetilde{q}}(\mathfrak{sl}(2,\mathbb{R}))\) ⋮ Positive Casimir and central characters of split real quantum groups ⋮ Toda conformal blocks, quantum groups, and flat connections ⋮ Quantum exponentials for the modular double and applications in gravity models ⋮ A cluster realization of \(U_q(\mathfrak {sl}_{\mathfrak {n}})\) from quantum character varieties ⋮ Positive representations with zero Casimirs ⋮ On tensor products of positive representations of split real quantum Borel subalgebra $\mathcal {U}_{q\widetilde {q}}(\mathfrak {b}_\mathbb {R})$ ⋮ On the continuous series for \(\widehat{sl(2,\mathbb R)}\) ⋮ Gauss-Lusztig decomposition for positive quantum groups and representation by \(q\)-tori ⋮ Tetrahedron equation and quantum \(R\) matrices for modular double of \(U_q(D^{(2)}_{n+1}), U_q (A ^{(2)}_{2n})\) and \(U_q(C^{(1)}_{n})\) ⋮ Cluster realization of positive representations of a split real quantum Borel subalgebra ⋮ Positive representations of split real simply-laced quantum groups

This page was built for publication: Positive Representations of Split Real Quantum Groups and Future Perspectives