Download A categori cation of the Temperley-Lieb algebra and Schur by Bernstein J. PDF

By Bernstein J.

Show description

Read or Download A categori
cation of the Temperley-Lieb algebra and Schur quotients of U(sl2) via projective and Zuckerman functors PDF

Best algebra books

College Algebra (9th Edition)

Collage Algebra, 9/E
Michael Sullivan, Chicago nation University
ISBN-10: 0321716817 • ISBN-13: 9780321716811
©2012 • Pearson • textile, 840 pp
Published 01/04/2011 • Instock

Suggested retail expense: $206. 00

Description
Mike Sullivan’s time-tested procedure focuses scholars at the primary talents they want for the direction: getting ready for sophistication, practising with homework, and reviewing the ideas. within the 9th variation, collage Algebra has developed to fulfill today’s path wishes, development on those hallmarks by way of integrating initiatives and different interactive studying instruments to be used within the school room or online.

New Internet-based bankruptcy tasks practice talents to real-world difficulties and are followed by way of assignable MathXL workouts to help you contain those tasks into the direction. furthermore, numerous new workout forms, exhibit Examples, and video tutorials for MathXL workouts supply teachers much more flexibility, whereas supporting scholars construct their conceptual knowing.

Fundamentals of Hopf Algebras (Universitext)

This article goals to supply graduate scholars with a self-contained advent to issues which are on the vanguard of contemporary algebra, specifically, coalgebras, bialgebras and Hopf algebras. The final bankruptcy (Chapter four) discusses a number of functions of Hopf algebras, a few of that are additional built within the author’s 2011 book, An creation to Hopf Algebras.

Group Theory and Its Applications, Volume II

Crew conception and its functions, quantity II covers the 2 extensive parts of purposes of workforce concept, specifically, all atomic and molecular phenomena, in addition to all points of nuclear constitution and ordinary particle conception. This quantity includes 5 chapters and starts with the illustration and tensor operators of the unitary teams.

Additional info for A categori
cation of the Temperley-Lieb algebra and Schur quotients of U(sl2) via projective and Zuckerman functors

Example text

Mat. Ser. III 32(52) (1997), 179–199. A. Rocha-Caridi. Splitting criteria for g-modules induced from a parabolic and the Bernstein-Gelfand-Gelfand resolution of a finite dimensional, irreducible g-module. Trans. AMS 262 (1980), 335–366. Yu. G. Turaev. Ribbon graphs and their invariants derived from quantum groups. Comm. Math. Phys. 127 (1990), 1–26. G. Turaev. Quantum Invariants of Knots and 3-Manifolds. De Gruyter Studies in Mathematics 18 (1994). V. Zelevinski. Small resolutions of singularities of Schubert varieties.

From now on we fix k between 0 and n. Let τii+1 be the composition of Ti and i+1 T : τii+1 = T i+1 ◦ Ti . This is a functor from Oµi to Oµi+1 . Similarly, let τii−1 be the functor from Oµi to Oµi−1 given by τii−1 = T i−1 ◦ Ti . Projective functors preserve subcategories of U (pk )-locally finite modules and thus k,n−k functors τii±1 restrict to functors from Oik,n−k to Oi±1 . Our categorification of the Temperley-Lieb algebra by projective functors is based on the following beautiful result of Enright and Shelton: k,n−k Theorem.

This is very much in line with the factorization of the element Ui of the Temperley-Lieb algebra as the composition ∪i,n−2 ◦ ∩i,n of morphisms ∪i,n−2 and ∩i,n of the Temperley-Lieb category. We now offer the reader a conjecture on realizing the Temperley-Lieb category via functors between parabolic categories Ok,n−k . Let ζn : O1k,n−k ∼ =✲ Ok−1,n−k−1 (60) be the Enright-Shelton equivalence of categories. Introduce functors ∩i,n :Ok,n−k −→ Ok−1,n−k−1 ∪i,n :Ok,n−k −→ Ok+1,n+1−k given by i−2 ∩i,n = ζn ◦ τ21 ◦ τ32 ◦ · · · ◦ τi−1 ◦ τii−1 ◦ T i ∪i,n = Ti ◦ i τi−1 ◦ i−1 τi−2 ···◦ τ23 ◦ τ12 ◦ −1 ζn+2 .

Download PDF sample

Rated 4.55 of 5 – based on 40 votes