Affine flag varieties and quantum symmetric pairs /

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 p...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Fan, Zhaobing (Autor), Lai, Chun-Ju (Autor), Li, Yiqiang (Autor), Luo, Li (Autor), Wang, Weiqiang, 1970- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, RI : American Mathematical Society, [2020]
Colección:Memoirs of the American Mathematical Society ; no. 1285.
Temas:
Flag manifolds.
Affine algebraic groups.
Quantum groups.
Schur complement.
Kazhdan-Lusztig polynomials.
Algebra, Homological.
Variétés de drapeaux (Géométrie)
Groupes algébriques affines.
Groupes quantiques.
Complément de Schur.
Polynômes de Kazhdan-Lusztig.
Algèbre homologique.
Grupos lineales algebraicos
Grupos cuánticos
Affine algebraic groups
Algebra, Homological
Flag manifolds
Kazhdan-Lusztig polynomials
Quantum groups
Schur complement
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.
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.
Algebraic geometry > (Colo.)homology theory [See also 13Dxx] > Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
Acceso en línea:Texto completo
Descripción
Sumario: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.
Notas:"May 2020, volume 265, number 1285 (second of 7 numbers)."
Descripción Física:1 online resource (v, 136 pages)
Bibliografía:Includes bibliographical references.
ISBN:9781470461386
1470461382

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