NDLI: Cluster structures on quantum coordinate rings

Content Provider	Springer Nature Link
Author	Schröer, J. Geiß, C. Leclerc, B.
Copyright Year	2012
Abstract	We show that the quantum coordinate ring of the unipotent subgroup N(w) of a symmetric Kac–Moody group G associated with a Weyl group element w has the structure of a quantum cluster algebra. This quantum cluster structure arises naturally from a subcategory $${\fancyscript{C}_{w}}$$ of the module category of the corresponding preprojective algebra. An important ingredient of the proof is a system of quantum determinantal identities that can be viewed as a q-analogue of a T-system. In case G is a simple algebraic group of type A, D, E, we deduce from these results that the quantum coordinate ring of an open cell of a partial flag variety attached to G also has a cluster structure.
Ending Page	397
Page Count	61
Starting Page	337
File Format	PDF
ISSN	10221824
e-ISSN	14209020
Journal	Selecta Mathematica
Issue Number	2
Volume Number	19
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2012-07-22
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Quantum group Representations of quivers and partially ordered sets Cluster algebras Quantum cluster algebra Preprojective algebra Quantum groups (quantized enveloping algebras) and related deformations Mathematics Quantum minor T-system
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy Mathematics

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Cluster structures on quantum coordinate rings