Compatibility of Drinfeld presentations for split affine Kac-Moody quantum symmetric pairs

Abstract

Let $(\mathbf{U},{\mathbf{U}}^{ı})$ be a split affine quantum symmetric pair of type ${\mathsf{B}}_n^{(1)},{\mathsf{C}}_n^{(1)}$ or ${\mathsf{D}}_n^{(1)}$. We prove factorization and coproduct formulae for the Drinfeld-Cartan operators ${\Theta }_i(z)$ in the Lu-Wang Drinfeld-type presentation, generalizing the type ${\mathsf{A}}_n^{(1)}$ result from [Prz23]. As an application, we show that a boundary analogue of the $q$-character map, defined via the spectra of these operators, is compatible with the usual $q$-character map. As an auxiliary result, we also produce explicit reduced expressions for the fundamental weights in the extended affine Weyl groups of classical types.

39 pages

References in corpus (7)

• Quantum symmetric Kac-Moody pairs
• Combinatorics of q-characters of finite-dimensional representations of quantum affine algebras
• Braid Group Action and Quantum Affine Algebras
• Canonical bases for tensor products and super Kazhdan-Lusztig theory
• Universal K-matrices for quantum Kac-Moody algebras
• A Drinfeld type presentation of affine $ı$quantum groups II: split BCFG type
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Cited by in corpus (1)

• Drinfeld rational fractions for affine Kac-Moody quantum symmetric pairs