Geometric Approach to I-Quantum Group of Affine Type D
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909131389009920 |
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| author | Chen, Quanyong Fan, Zhaobing |
| author_facet | Chen, Quanyong Fan, Zhaobing |
| contents | In this paper, we study the structures of Schur algebra and Lusztig algebra associated to partial flag varieties of affine type D. We show that there is a subalgebra of Lusztig algebra and the quantum groups arising from this subalgebras via stabilization procedures is a coideal subalgebra of quantum group of affine $\mathfrak{sl}$ type. We construct monomial and canonical bases of the idempotented quantum algebra and establish the positivity properties of the canonical basis with respect to multiplication and the bilinear pairing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04461 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric Approach to I-Quantum Group of Affine Type D Chen, Quanyong Fan, Zhaobing Quantum Algebra Representation Theory In this paper, we study the structures of Schur algebra and Lusztig algebra associated to partial flag varieties of affine type D. We show that there is a subalgebra of Lusztig algebra and the quantum groups arising from this subalgebras via stabilization procedures is a coideal subalgebra of quantum group of affine $\mathfrak{sl}$ type. We construct monomial and canonical bases of the idempotented quantum algebra and establish the positivity properties of the canonical basis with respect to multiplication and the bilinear pairing. |
| title | Geometric Approach to I-Quantum Group of Affine Type D |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2403.04461 |