Details

Subject(s)

• Hecke algebras [Browse]
• Schur complement [Browse]
• Affine algebraic groups [Browse]
• Quantum groups [Browse]

Series

• Memoirs of the American Mathematical Society ; Volume 281. [More in this series]
• Memoirs of the American Mathematical Society Series ; Volume 281 [More in this series]

Summary note

"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.

Bibliographic references

Includes bibliographical references.

Source of description

• Description based on publisher supplied metadata and other sources.
• Description based on print version record.

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.

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ISBN

• 9781470473198
• 1470473194

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