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020 a| 9781470456269q| (paperback);

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100 1 a| Fan, Zhaobing.?| UNAUTHORIZED;

245 10 a| Affine Hecke algebras and quantum symmetric pairsh| [electronic resource] /c| Zhaobing Fan, Chun-Ju Lai, Yiqiang Li, Li Luo, Weiqiang Wang.;

260 a| Providence, RI :b| AMS, American Mathematical Society,c| 2023.;

300 a| ix, 92 pages :b| illustrations ;c| 26 cm;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| volume 281, number 1386;

504 a| Includes bibliographical references (pages 91-92).;

505 0 a| Affine Schur algebras via affine Hecke algebras -- Multiplication formula for affine Hecke algebra -- Multiplication formula for affine Schur algebra -- Monomial and canonical bases for affine Schur algebra -- Stabilization algebra Kcn arising from affine Schur algebras -- The quantum symmetric pair (Kn,Kcn) -- Stabilization algebras arising from other Schur algebras.;

506 a| Available only to authorized users.;

520 a| "We introduce an affine Schur algebra via the affine Hecke algebra associated to Weyl group of affine type C. We establish multiplication formulas on the affine Hecke algebra and affine Schur algebra. Then we construct monomial bases and canonical bases for the affine Schur algebra. The multiplication formula allows us to establish a stabilization property of the family of affine Schur algebras that leads to the modified version of an algebra Kc n. We show that Kc n is a coideal subalgebra of quantum affine algebra Uppglnq, and Uppglnq,Kc nq forms a quantum symmetric pair. The modified coideal subalgebra is shown to admit monomial and stably canonical bases. We also formulate several variants of the affine Schur algebra and the (modified) coideal subalgebra above, as well as their monomial and canonical bases. This work provides a new and algebraic approach which complements and sheds new light on our previous geometric approach on the subject. In the appendix by four of the authors, new length formulas for the Weyl groups of affine classical types are obtained in a symmetrized fashion"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Hecke algebras.=| ^A257598;

650 0 a| Schur complement.=| ^A879589;

650 0 a| Affine algebraic groups.=| ^A597019;

650 0 a| Quantum groups.=| ^A307279;

650 7 a| Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Representations, algebraic theory (weights).2| msc;

650 7 a| Group theory and generalizations -- Linear algebraic groups and related topics -- Quantum groups (quantized function algebras) and their representations.2| msc;

650 7 a| Group theory and generalizations -- Linear algebraic groups and related topics -- Schur and $q$-Schur algebras.2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Lai, Chun-Ju.?| UNAUTHORIZED;

700 1 a| Li, Yiqiang.?| UNAUTHORIZED;

700 1 a| Luo, Li.?| UNAUTHORIZED;

700 1 a| Wang, Weiqiang,d| 1970-=| ^A1104121;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=30330567;

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Affine Hecke algebras and quantum symmetric pairs / Zhaobing Fan, Chun-Ju Lai, Yiqiang Li, Li Luo, Weiqiang Wang.

Author/creator	Fan, Zhaobing
Format	Electronic
Publication Info	Providence, RI : AMS, American Mathematical Society, 2023.
Description	ix, 92 pages : illustrations ; 26 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Hecke algebras. Schur complement. Affine algebraic groups. Quantum groups.

Other author/creator	Lai, Chun-Ju.
Other author/creator	Li, Yiqiang.
Other author/creator	Luo, Li.
Other author/creator	Wang, Weiqiang, 1970-
Series	Memoirs of the American Mathematical Society, 0065-9266 ; volume 281, number 1386
Contents	Affine Schur algebras via affine Hecke algebras -- Multiplication formula for affine Hecke algebra -- Multiplication formula for affine Schur algebra -- Monomial and canonical bases for affine Schur algebra -- Stabilization algebra Kcn arising from affine Schur algebras -- The quantum symmetric pair (Kn,Kcn) -- Stabilization algebras arising from other Schur algebras.
Abstract	"We introduce an affine Schur algebra via the affine Hecke algebra associated to Weyl group of affine type C. We establish multiplication formulas on the affine Hecke algebra and affine Schur algebra. Then we construct monomial bases and canonical bases for the affine Schur algebra. The multiplication formula allows us to establish a stabilization property of the family of affine Schur algebras that leads to the modified version of an algebra Kc n. We show that Kc n is a coideal subalgebra of quantum affine algebra Uppglnq, and Uppglnq,Kc nq forms a quantum symmetric pair. The modified coideal subalgebra is shown to admit monomial and stably canonical bases. We also formulate several variants of the affine Schur algebra and the (modified) coideal subalgebra above, as well as their monomial and canonical bases. This work provides a new and algebraic approach which complements and sheds new light on our previous geometric approach on the subject. In the appendix by four of the authors, new length formulas for the Weyl groups of affine classical types are obtained in a symmetrized fashion"-- Provided by publisher.
Bibliography note	Includes bibliographical references (pages 91-92).
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2023011876
ISBN	9781470456269 (paperback)
ISBN	(pdf)

Affine Hecke algebras and quantum symmetric pairs / Zhaobing Fan, Chun-Ju Lai, Yiqiang Li, Li Luo, Weiqiang Wang.

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