Universal Verma Modules and the Misra-Miwa Fock Space
The Misra-Miwa v-deformed Fock space is a representation of the quantized affine algebra Uv(sl^ℓ). It has a standard basis indexed by partitions, and the nonzero matrix entries of the action of the Chevalley generators with respect to this basis are powers of v. Partitions also index the polynomial...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/326247 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832552391558299648 |
|---|---|
| author | Arun Ram Peter Tingley |
| author_facet | Arun Ram Peter Tingley |
| author_sort | Arun Ram |
| collection | DOAJ |
| description | The Misra-Miwa v-deformed Fock space is a representation of the quantized affine algebra Uv(sl^ℓ). It has a standard basis indexed by partitions, and the nonzero matrix
entries of the action of the Chevalley generators with respect to this basis are powers of v. Partitions also index the polynomial Weyl modules for Uq(glN) as N tends to infinity. We explain how the powers of v which appear in the Misra-Miwa Fock space also appear naturally
in the context of Weyl modules. The main tool we use is the Shapovalov determinant for a
universal Verma module. |
| format | Article |
| id | doaj-art-cd9f689a2ee549d9ba7e70445148c53f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-cd9f689a2ee549d9ba7e70445148c53f2025-02-03T05:58:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/326247326247Universal Verma Modules and the Misra-Miwa Fock SpaceArun Ram0Peter Tingley1Department of Mathematics and Statistics, University of Melbourne, Parkville VIC 3010, AustraliaDepartment of Mathematics, MIT, 77 Massachusetts Ave, Cambridge, MA 02139, USAThe Misra-Miwa v-deformed Fock space is a representation of the quantized affine algebra Uv(sl^ℓ). It has a standard basis indexed by partitions, and the nonzero matrix entries of the action of the Chevalley generators with respect to this basis are powers of v. Partitions also index the polynomial Weyl modules for Uq(glN) as N tends to infinity. We explain how the powers of v which appear in the Misra-Miwa Fock space also appear naturally in the context of Weyl modules. The main tool we use is the Shapovalov determinant for a universal Verma module.http://dx.doi.org/10.1155/2010/326247 |
| spellingShingle | Arun Ram Peter Tingley Universal Verma Modules and the Misra-Miwa Fock Space International Journal of Mathematics and Mathematical Sciences |
| title | Universal Verma Modules and the Misra-Miwa Fock Space |
| title_full | Universal Verma Modules and the Misra-Miwa Fock Space |
| title_fullStr | Universal Verma Modules and the Misra-Miwa Fock Space |
| title_full_unstemmed | Universal Verma Modules and the Misra-Miwa Fock Space |
| title_short | Universal Verma Modules and the Misra-Miwa Fock Space |
| title_sort | universal verma modules and the misra miwa fock space |
| url | http://dx.doi.org/10.1155/2010/326247 |
| work_keys_str_mv | AT arunram universalvermamodulesandthemisramiwafockspace AT petertingley universalvermamodulesandthemisramiwafockspace |