NDLI: MODULES FOR RELATIVE YANGIANS (FAMILY ALGEBRAS) AND KAZHDAN-LUSZTIG POLYNOMIALS

Content Provider	Springer Nature Link
Author	JOSEPH, ANTHONY
Copyright Year	2014
Abstract	Let g be a complex simple Lie algebra and let mod U (g) be the category of finite dimensional U (g)-modules. The relative Yangian Y V (g) with respect to the pair g, V: V ∈ mod U (g) is defined to be the g invariant subalgebra of End V ⊗ U (g) with respect to the natural “diagonal” action. According to recent work (see [12, Sect. 5] and references therein), the finite dimensional simple modules of the Yangians for g = sl(n) or the twisted Yangians for g = sp(2n), so(n) are described by the simple modules of relative Yangians Y V (g) : V ∈ mod U (g). Here a classification of the simple modules of a relative Yangian is obtained simply and briefly as an advanced exercise in Frobenius reciprocity inspired by a Bernstein–Gelfand equivalence of categories [2]. An unexpected fact is that the dimension of these modules are determined by the Kazhdan-Lusztig polynomials, and conversely the latter are described in terms of dimensions of certain extension groups associated to finite dimensional modules of relative Yangians.
Starting Page	105
Ending Page	129
Page Count	25
File Format	PDF
ISSN	10834362
Journal	Transformation Groups
Volume Number	19
Issue Number	1
e-ISSN	1531586X
Language	English
Publisher	Springer US
Publisher Date	2014-02-15
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Topological Groups, Lie Groups Algebra
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Geometry and Topology

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