A categorification of the Temperley-Lieb algebra and Schur quotients of U(sl2) via projective and Zuckerman functors
نویسندگان
چکیده
2.1. U̇(sl2) and its representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 2.1.1. Algebra U̇(sl2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 2.1.2. Representations of U̇(sl2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 2.2. Temperley-Lieb algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 2.3. The category of highest weight modules over a reductive Lie algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 2.3.1. Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 2.3.2. Projective functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 2.3.3. Parabolic categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 2.3.4. Zuckerman functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 2.4. Singular blocks of the highest weight category for gln . . . . . . . . . . . . 214 2.4.1. Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 2.4.2. Simple and projective module bases in the Grothendieck group K(On) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
منابع مشابه
Category O and sl(k) link invariants
The program of categorification via category O was introduced by J. Bernstein, I. Frenkel, and M. Khovanov in [BFK] where tensor powers of the standard two dimensional representation of sl2 were recognized as Grothendieck groups of certain subcategories of O for various gln. They had two different constructions. One was based on studying certain blocks with singular generalized central characte...
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