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Quantum Deformation of the Grassmannian Manifold

✍ Scribed by R. Fioresi

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
202 KB
Volume
214
Category
Article
ISSN
0021-8693

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✦ Synopsis

In this paper we work out a deformation of G r, n , the grassmannian of r-subspaces in a vector space of dimension n over a field k of characteristic 0. Ε½ . Ε½ . G r, n is deformed as an homogeneous space for SL k , the special linear group n n w Ε½ .x Ε½ . of k ; this means that k G r, n , the coordinate ring of G r, n , gets deformed w x Ε½ . together with with the coaction of k SL , the coordinate ring of SL k , on it.

n n

Our deformation comes together with a coaction of the corresponding deformation Ε½ . of SL k . At the end we give an explicit presentation of the deformed grassmann nian, in terms of generators and relations.

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