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Quantum deformation of flag schemes and Grassmann schemes. I: A \(q\)- deformation of the shape-algebra for \(GL(n)\). (English) Zbl 0739.17007

The authors construct \(q\)-deformations of the affine Grassmann and flag varieties over the quantum general and special linear groups. Here \(q\)- deformations mean deformations of the coordinate rings of the appropriate varieties. This is done by deforming the relations given by the second author [in J. Algebra 47, 80-104 (1977; Zbl 0358.15033) and ibid. 61, 414-462 (1979; Zbl 0437.14030)].

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
14M17 Homogeneous spaces and generalizations
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