On the geometric realization of the inner product and canonical basis for quantum affine $\mathfrak{sl}_n$
We give a geometric interpretation of the inner product on the modified quantum group of $\hat{\mathfrak{sl}}_n$. We also give some applications of this interpretation, including a positivity result for the inner product, and a new geometric construction of the canonical basis.
| Main Author: | |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
2010
|
| _version_ | 1797065346372337664 |
|---|---|
| author | McGerty, K |
| author_facet | McGerty, K |
| author_sort | McGerty, K |
| collection | OXFORD |
| description | We give a geometric interpretation of the inner product on the modified quantum group of $\hat{\mathfrak{sl}}_n$. We also give some applications of this interpretation, including a positivity result for the inner product, and a new geometric construction of the canonical basis. |
| first_indexed | 2024-03-06T21:27:20Z |
| format | Journal article |
| id | oxford-uuid:43897e80-bb8a-4df7-89da-71bfbd35af1b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:27:20Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:43897e80-bb8a-4df7-89da-71bfbd35af1b2022-03-26T14:56:03ZOn the geometric realization of the inner product and canonical basis for quantum affine $\mathfrak{sl}_n$Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:43897e80-bb8a-4df7-89da-71bfbd35af1bEnglishSymplectic Elements at Oxford2010McGerty, KWe give a geometric interpretation of the inner product on the modified quantum group of $\hat{\mathfrak{sl}}_n$. We also give some applications of this interpretation, including a positivity result for the inner product, and a new geometric construction of the canonical basis. |
| spellingShingle | McGerty, K On the geometric realization of the inner product and canonical basis for quantum affine $\mathfrak{sl}_n$ |
| title | On the geometric realization of the inner product and canonical basis
for quantum affine $\mathfrak{sl}_n$ |
| title_full | On the geometric realization of the inner product and canonical basis
for quantum affine $\mathfrak{sl}_n$ |
| title_fullStr | On the geometric realization of the inner product and canonical basis
for quantum affine $\mathfrak{sl}_n$ |
| title_full_unstemmed | On the geometric realization of the inner product and canonical basis
for quantum affine $\mathfrak{sl}_n$ |
| title_short | On the geometric realization of the inner product and canonical basis
for quantum affine $\mathfrak{sl}_n$ |
| title_sort | on the geometric realization of the inner product and canonical basis for quantum affine mathfrak sl n |
| work_keys_str_mv | AT mcgertyk onthegeometricrealizationoftheinnerproductandcanonicalbasisforquantumaffinemathfraksln |