| Description |
1 online resource (v, 136 pages) |
| Series |
Memoirs of the American Mathematical Society ; number 1285 |
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Memoirs of the American Mathematical Society ; no. 1285.
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| Contents |
Constructions in affine type A -- Lattice presentation of affine flag varieties of type C -- Multiplication formulas for Chevalley generators -- Coideal algebra type structures of Schur algebras and Lusztig algebras -- Realization of the idempotented coideal subalgebra Uc/n of U(sln) -- A second coideal subalgebra of quantum affine sln -- More variants of coideal subalgebras of quantum affine sln -- The stabilization algebra Kc/n arising from Schur algebras -- Stabilization algebras arising from other Schur algebras |
| Summary |
The quantum groups of finite and affine type admit geometric realizations in terms of partial flag varieties of finite and affine type . Recently, the quantum group associated to partial flag varieties of finite type is shown to be a coideal subalgebra of the quantum group of finite type . In this paper we study the structures of Schur algebras and Lusztig algebras associated to (four variants of) partial flag varieties of affine type . We show that the quantum groups arising from Lusztig algebras and Schur algebras via stabilization procedures are (idempotented) coideal subalgebras of quantum groups of affine and types, respectively. In this way, we provide geometric realizations of eight quantum symmetric pairs of affine types. We construct monomial and canonical bases of all these quantum (Schur, Lusztig, and coideal) algebras. For the idempotented coideal algebras of affine type, we establish the positivity properties of the canonical basis with respect to multiplication, comultiplication and a bilinear pairing. In particular, we obtain a new and geometric construction of the idempotented quantum affine and its canonical basis |
| Notes |
"May 2020, volume 265, number 1285 (second of 7 numbers)." |
| Bibliography |
Includes bibliographical references |
| Notes |
Description based on print version record |
| Subject |
Flag manifolds.
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Affine algebraic groups.
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Quantum groups.
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Schur complement.
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Kazhdan-Lusztig polynomials.
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Algebra, Homological.
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Grupos lineales algebraicos
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Grupos cuánticos
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Affine algebraic groups
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Algebra, Homological
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Flag manifolds
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Kazhdan-Lusztig polynomials
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Quantum groups
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Schur complement
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Nonassociative rings and algebras -- Lie algebras and Lie superalgebras {For Lie groups, see 22Exx} -- Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 8.
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Group theory and generalizations -- Linear algebraic groups and related topics {For arithmetic theory, see 11E57, 11H56; for geometric theory, see 14Lxx, 22Exx; for other methods in representation the.
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Algebraic geometry -- (Colo.)homology theory [See also 13Dxx] -- Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
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| Form |
Electronic book
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| Author |
Lai, Chun-Ju, author.
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Li, Yiqiang, author.
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Luo, Li, author.
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Wang, Weiqiang, 1970- author.
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| ISBN |
9781470461386 |
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1470461382 |
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