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Abstract We explicitly determine the defining relations of all quantum symmetric pair coideal subalgebras of quantised enveloping algebras of Kac–Moody type. Our methods are based on star products on noncommutative $${\mathbb N}$$ -graded algebras. The resulting defining relations are expressed in terms of continuous q -Hermite polynomials and a new family of deformed Chebyshev polynomials.
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Quantum Q -Systems and Fermionic Sums—The Non-Simply Laced Case
Abstract In this paper, we seek to prove the equality of the $$q$$-graded fermionic sums conjectured by Hatayama et al. [ 14] in its full generality, by extending the results of Di Francesco and Kedem [ 9] to the non-simply laced case. To this end, we will derive explicit expressions for the quantum $$Q$$-system relations, which are quantum cluster mutations that correspond to the classical $$Q$$-system relations, and write the identity of the $$q$$-graded fermionic sums as a constant term identity. As an application, we will show that these quantum $$Q$$-system relations are consistent with the short exact sequence of the Feigin–Loktev fusion product of Kirillov–Reshetikhin modules obtained by Chari and Venkatesh [ 5].
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- Award ID(s):
- 1937241
- PAR ID:
- 10232940
- Date Published:
- Journal Name:
- International Mathematics Research Notices
- Volume:
- 2021
- Issue:
- 2
- ISSN:
- 1073-7928
- Page Range / eLocation ID:
- 805 to 854
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/imrn/rnaa198
