Crystals and affine Hecke algebras of type D
The Lascoux-Leclerc-Thibon-Ariki theory asserts that the K-group of the representations of the affine Hecke algebras of type A is isomorphic to the algebra of functions on the maximal unipotent subgroup of the group associated with a Lie algebra $g$ where $g$ is $gl_\infty$ or the affine Lie algebra...
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| Format: | Journal article |
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2007
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| _version_ | 1826286720793968640 |
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| author | Kashiwara, M Miemietz, V |
| author_facet | Kashiwara, M Miemietz, V |
| author_sort | Kashiwara, M |
| collection | OXFORD |
| description | The Lascoux-Leclerc-Thibon-Ariki theory asserts that the K-group of the representations of the affine Hecke algebras of type A is isomorphic to the algebra of functions on the maximal unipotent subgroup of the group associated with a Lie algebra $g$ where $g$ is $gl_\infty$ or the affine Lie algebra $A^{(1)}_\ell$, and the irreducible representations correspond to the upper global bases. Recently, N. Enomoto and the first author presented the notion of symmetric crystals and formulated analogous conjectures for the affine Hecke algebras of type B. In this note, we present similar conjectures for certain classes of irreducible representations of affine Hecke algebras of type D. The crystal for type D is a double cover of the one for type B. |
| first_indexed | 2024-03-07T01:47:56Z |
| format | Journal article |
| id | oxford-uuid:99102f7d-afd1-48c7-8c68-3c9252709445 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T01:47:56Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:99102f7d-afd1-48c7-8c68-3c92527094452022-03-27T00:11:32ZCrystals and affine Hecke algebras of type DJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:99102f7d-afd1-48c7-8c68-3c9252709445Symplectic Elements at Oxford2007Kashiwara, MMiemietz, VThe Lascoux-Leclerc-Thibon-Ariki theory asserts that the K-group of the representations of the affine Hecke algebras of type A is isomorphic to the algebra of functions on the maximal unipotent subgroup of the group associated with a Lie algebra $g$ where $g$ is $gl_\infty$ or the affine Lie algebra $A^{(1)}_\ell$, and the irreducible representations correspond to the upper global bases. Recently, N. Enomoto and the first author presented the notion of symmetric crystals and formulated analogous conjectures for the affine Hecke algebras of type B. In this note, we present similar conjectures for certain classes of irreducible representations of affine Hecke algebras of type D. The crystal for type D is a double cover of the one for type B. |
| spellingShingle | Kashiwara, M Miemietz, V Crystals and affine Hecke algebras of type D |
| title | Crystals and affine Hecke algebras of type D |
| title_full | Crystals and affine Hecke algebras of type D |
| title_fullStr | Crystals and affine Hecke algebras of type D |
| title_full_unstemmed | Crystals and affine Hecke algebras of type D |
| title_short | Crystals and affine Hecke algebras of type D |
| title_sort | crystals and affine hecke algebras of type d |
| work_keys_str_mv | AT kashiwaram crystalsandaffineheckealgebrasoftyped AT miemietzv crystalsandaffineheckealgebrasoftyped |