cation of the Temperley-Lieb algebra and Schur PDF

By Bernstein J.

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cation of the Temperley-Lieb algebra and Schur quotients of U(sl2) via projective and Zuckerman functors PDF

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cation of the Temperley-Lieb algebra and Schur quotients of U(sl2) via projective and Zuckerman functors

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Fischer. 2-categories and 2-knots. Duke Math J. 75 (1994), 493–526. B. Frenkel and M. Khovanov. Canonical bases in tensor products and graphical calculus for Uq (sl2 ). Duke Math J. 87 (1997), 409–480. B. Frenkel, M. Khovanov and A. Kirillov, Jr. Kazhdan-Lusztig polynomials and canonical basis. Transformation Groups 3 (1998), 321–336. K. M. Green. Monomials and Temperley-Lieb algebras. J. Algebra 190 (1997), 498–517. B. Frenkel and F. Malikov. Annihilating ideals and tilting functors. Preprint qalg/9801065.

Corollary 6. The categories Ok,n−k Denote by Ξn,i the equivalence of categories i Ξn,i : Ok,n−k −→ Ok−1,n−k−1 given by the composition Ξn,i = νn ◦ Γ11 ◦ ε2 ◦ Γ12 ◦ . . , Ξn,i is the composition of equivalences of categories i Ok,n−k ∼ =✲ i−1 Ok,n−k ∼ =✲ ... ∼ =✲ 1 Ok,n−k ∼ =✲ Ok−1,n−k−1 . Denote by Πn,i the equivalence of categories i Πn,i : Ok,n−k −→ Ok+1,n+1−k given by Πn,i = Γ1i ◦ εi−1 ◦ Γ1i−1 ◦ · · · ◦ ε2 ◦ Γ12 ◦ ε1 ◦ ςn . Denote the derived functors of these functors by RΞn,i and RΠn,i . Define functors ∩i,n :Db (Ok,n−k ) −→ Db (Ok−1,n−k−1 ) ∪i,n :Db (Ok,n−k ) −→ Db (Ok+1,n+1−k ) by ∩i,n = RΞn,i ◦ RΓi [1] (58) ∪i,n = εi ◦ RΠn,i .

Math. Phys. 35 (1994), 5136–5154. J. Enright and B. Shelton. Memoirs of the AMS 367 (1987), Categories of highest weight modules: applications to classical Hermitian symmetric pairs. J. R. Wallach. Notes on homological algebra and representations of Lie algebras. Duke Math. Jour. 47 (1980), 1–15. J. Fischer. 2-categories and 2-knots. Duke Math J. 75 (1994), 493–526. B. Frenkel and M. Khovanov. Canonical bases in tensor products and graphical calculus for Uq (sl2 ). Duke Math J. 87 (1997), 409–480.

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A categori
cation of the Temperley-Lieb algebra and Schur quotients of U(sl2) via projective and Zuckerman functors by Bernstein J.


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