تقرير
Cluster structures on quantum coordinate rings
| العنوان: | Cluster structures on quantum coordinate rings |
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| المؤلفون: | Geiss, C., Leclerc, B., Schröer, J. |
| المصدر: | Selecta Mathematica: Volume 19, Issue 2 (2013), 337-397 |
| سنة النشر: | 2011 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Quantum Algebra, Mathematics - Rings and Algebras, Mathematics - Representation Theory |
| الوصف: | We show that the quantum coordinate ring of the unipotent subgroup N(w) of a symmetric Kac-Moody group G associated with a Weyl group element w has the structure of a quantum cluster algebra. This quantum cluster structure arises naturally from a subcategory C_w of the module category of the corresponding preprojective algebra. An important ingredient of the proof is a system of quantum determinantal identities which can be viewed as a q-analogue of a T-system. In case G is a simple algebraic group of type A, D, E, we deduce from these results that the quantum coordinate ring of an open cell of a partial flag variety attached to G also has a cluster structure. Comment: v2: minor corrections. v3: references updated, final version to appear in Selecta Mathematica |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s00029-012-0099-x |
| URL الوصول: | http://arxiv.org/abs/1104.0531 |
| رقم الأكسشن: | edsarx.1104.0531 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s00029-012-0099-x |
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