Presenting Schur Algebras as Quotients of the Universal Enveloping Algebra of gl2
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
We give a presentation of the Schur algebras S Q (2,d) by generators and relations, in fact a presentation which is compatible with Serre's presentation of the universal enveloping algebra of a simple Lie algebra. In the process we find a new basis for S Q (2,d), a truncated form of the usual PBW basis. We also locate the integral Schur algebra within the presented algebra as the analogue of Kostant's Z-form, and show that it has an integral basis which is a truncated version of Kostant's basis.
- Carter, R. and Lusztig, G.: On the modular representations of the general linear and symmetric groups, Math. Z. 136 (1974), 193–242.
- Donkin, S.: On Schur algebras and related algebras III: integral representations, Math. Proc. Cambridge Philos. Soc. 116 (1994), 37–55.
- Doty, S. R. and Giaquinto, A.: Presenting quantum Schur algebras as quotients of the quantized universal enveloping algebra of gl2, Preprint, Loyola Univ. Chicago, Sept. 2000.
- Green, J. A.: Polynomial Representations of GLn, Lecture Notes in Math. 830, Springer-Verlag, New York, 1980.
- Green, R.: q-Schur algebras as quotients of quantized enveloping algebras, J. Algebra 185 (1996), 660–687.
- Jantzen, J. C.: Representations of Algebraic Groups, Academic Press, Orlando, 1987.
- Kostant, B.: Groups over ℤ, Proc. Sympos. Pure Math. 9 (1966), 90–98.
- Presenting Schur Algebras as Quotients of the Universal Enveloping Algebra of gl2
Algebras and Representation Theory
Volume 7, Issue 1 , pp 1-17
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- Schur algebra
- enveloping algebra
- generators and relations