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Based Ring of Two-Sided Cells of Affine Weyl Groups of Type ̃A_{n-1}.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2002Copyright date: ©2002Edition: 1st edDescription: 1 online resource (114 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470403423
Subject(s): Genre/Form: Additional physical formats: Print version:: Based Ring of Two-Sided Cells of Affine Weyl Groups of Type ̃A_{n-1}DDC classification:
  • 510 s;512/.55
LOC classification:
  • QA174.2 -- .X5 2002eb
Online resources:
Contents:
Intro -- Contents -- Introduction -- Chapter 1. Cells in Affine Weyl Groups -- 1.1. Hecke algebra -- 1.2. Cell and a-function -- 1.3. Affine Weyl group -- 1.4. Star operation -- 1.5. Based ring -- 1.6. Star operation, II -- Chapter 2. Type A[sub(n-1)] -- 2.1. The affine Weyl group associated with GL[sub(n)](C) -- 2.2. Cells -- 2.3. The based ring J[sub(c)] -- 2.4. Chains and antichains -- 2.5. Star operations for W -- Chapter 3. Canonical Left Cells -- 3.1. The dominant weights -- 3.2. The right cell containing x ∈ X[sup(+)] -- 3.3. The elements m[sub(x)] -- 3.4. The distinguished involutions -- Chapter 4. The Group F[sup(λ)] and Its Representation -- 4.1. The group F[sub(λ)] -- 4.2. The representation ring of F[sub(λ)] -- Chapter 5. A Bijection Between T[sub(λ)] ∩ Γ[sup(-1)][sub(λ)] And IrrF[sub(λ)] -- 5.1. r-antichains of elements in Γ[sub(λ)] &amp -- #8745 Γ[sup(-1)][sup(λ)] -- 5.2. A map from Γ[sub(λ)] &amp -- #8745 Γ[sup(-1)][sup(λ)] to Dom(F[sub(λ)]) -- 5.3. Constructing elements of Γ[sub(λ)] &amp -- #8745 Γ[sup(-1)][sup(λ)] -- 5.4. Some simple properties of elements in Γ[sub(λ)] &amp -- #8745 Γ[sup(-1)][sup(λ)] -- 5.5. Some elements of Γ[sub(λ)] &amp -- #8745 Γ[sup(-1)][sup(λ)] -- Chapter 6. A Factorization Formula in J[sub(Γ[sub(λ)] &amp -- #8745 Γ[sup(-1)][sup(λ)])] -- 6.1. The integers γ[sub(u,v,w)] -- 6.2. A computation for some T[sub(u)]T[sub(v)] -- 6.3. Some consequences -- 6.4. The factorization formula -- Chapter 7. A Multiplication Formula in J[sub(Γ[sub(λ)] &amp -- #8745 Γ[sup(-1)][sup(λ)])] -- 7.1. A computation for some T[sub(u)]T[sub(v)] -- 7.2. A multiplication formula -- Chapter 8. The Based Rings J[sub(Γ[sub(λ)] &amp -- #8745 Γ[sup(-1)][sup(λ)])] and J[sub(c)] -- 8.1. Some lemmas -- 8.2. The based ring J[sub(Γ[sub(λ)] &amp -- #8745 Γ[sup(-1)][sup(λ)])] and the based ring J[sub(c)] -- 8.3. PGL[sub(n)](C).
8.4. SL[sub(n)](C) -- Bibliography -- Index -- Notation.
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Intro -- Contents -- Introduction -- Chapter 1. Cells in Affine Weyl Groups -- 1.1. Hecke algebra -- 1.2. Cell and a-function -- 1.3. Affine Weyl group -- 1.4. Star operation -- 1.5. Based ring -- 1.6. Star operation, II -- Chapter 2. Type A[sub(n-1)] -- 2.1. The affine Weyl group associated with GL[sub(n)](C) -- 2.2. Cells -- 2.3. The based ring J[sub(c)] -- 2.4. Chains and antichains -- 2.5. Star operations for W -- Chapter 3. Canonical Left Cells -- 3.1. The dominant weights -- 3.2. The right cell containing x ∈ X[sup(+)] -- 3.3. The elements m[sub(x)] -- 3.4. The distinguished involutions -- Chapter 4. The Group F[sup(λ)] and Its Representation -- 4.1. The group F[sub(λ)] -- 4.2. The representation ring of F[sub(λ)] -- Chapter 5. A Bijection Between T[sub(λ)] ∩ Γ[sup(-1)][sub(λ)] And IrrF[sub(λ)] -- 5.1. r-antichains of elements in Γ[sub(λ)] &amp -- #8745 Γ[sup(-1)][sup(λ)] -- 5.2. A map from Γ[sub(λ)] &amp -- #8745 Γ[sup(-1)][sup(λ)] to Dom(F[sub(λ)]) -- 5.3. Constructing elements of Γ[sub(λ)] &amp -- #8745 Γ[sup(-1)][sup(λ)] -- 5.4. Some simple properties of elements in Γ[sub(λ)] &amp -- #8745 Γ[sup(-1)][sup(λ)] -- 5.5. Some elements of Γ[sub(λ)] &amp -- #8745 Γ[sup(-1)][sup(λ)] -- Chapter 6. A Factorization Formula in J[sub(Γ[sub(λ)] &amp -- #8745 Γ[sup(-1)][sup(λ)])] -- 6.1. The integers γ[sub(u,v,w)] -- 6.2. A computation for some T[sub(u)]T[sub(v)] -- 6.3. Some consequences -- 6.4. The factorization formula -- Chapter 7. A Multiplication Formula in J[sub(Γ[sub(λ)] &amp -- #8745 Γ[sup(-1)][sup(λ)])] -- 7.1. A computation for some T[sub(u)]T[sub(v)] -- 7.2. A multiplication formula -- Chapter 8. The Based Rings J[sub(Γ[sub(λ)] &amp -- #8745 Γ[sup(-1)][sup(λ)])] and J[sub(c)] -- 8.1. Some lemmas -- 8.2. The based ring J[sub(Γ[sub(λ)] &amp -- #8745 Γ[sup(-1)][sup(λ)])] and the based ring J[sub(c)] -- 8.3. PGL[sub(n)](C).

8.4. SL[sub(n)](C) -- Bibliography -- Index -- Notation.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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