Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | 오세진 | * |
dc.date.accessioned | 2022-06-02T16:31:26Z | - |
dc.date.available | 2022-06-02T16:31:26Z | - |
dc.date.issued | 2022 | * |
dc.identifier.issn | 0075-4102 | * |
dc.identifier.other | OAK-31332 | * |
dc.identifier.uri | https://dspace.ewha.ac.kr/handle/2015.oak/261319 | - |
dc.description.abstract | Let g{\mathfrak{g},\mathsf{g})} be a pair of complex finite-dimensional simple Lie algebras whose Dynkin diagrams are related by (un)folding, with - {\mathsf{g}} being of simply-laced type. We construct a collection of ring isomorphisms between the quantum Grothendieck rings of monoidal categories cg\mathscr{C}_{\mathfrak{g}}} and c - {\mathscr{C}_{\mathsf{g}}} of finite-dimensional representations over the quantum loop algebras of g{\mathfrak{g}} and - {\mathsf{g}}, respectively. As a consequence, we solve long-standing problems: the positivity of the analogs of Kazhdan-Lusztig polynomials and the positivity of the structure constants of the quantum Grothendieck rings for any non-simply-laced g{\mathfrak{g}}. In addition, comparing our isomorphisms with the categorical relations arising from the generalized quantum affine Schur-Weyl dualities, we prove the analog of Kazhdan-Lusztig conjecture (formulated in [D. Hernandez, Algebraic approach to q,tq,t-characters, Adv. Math. 187 2004, 1, 1-52]) for simple modules in remarkable monoidal subcategories of cg{\mathscr{C}_{\mathfrak{g}}} for any non-simply-laced g{\mathfrak{g}}, and for any simple finite-dimensional modules in cg{\mathscr{C}_{\mathfrak{g}}} for g{\mathfrak{g}} of type Bn{\mathrm{B}_{n}}. In the course of the proof we obtain and combine several new ingredients. In particular, we establish a quantum analog of T-systems, and also we generalize the isomorphisms of [D. Hernandez and B. Leclerc, Quantum Grothendieck rings and derived Hall algebras, J. reine angew. Math. 701 2015, 77-126, D. Hernandez and H. Oya, Quantum Grothendieck ring isomorphisms, cluster algebras and Kazhdan-Lusztig algorithm, Adv. Math. 347 2019, 192-272] to all g{\mathfrak{g}} in a unified way, that is, isomorphisms between subalgebras of the quantum group of - {\mathsf{g}} and subalgebras of the quantum Grothendieck ring of cg{\mathscr{C}_{\mathfrak{g}}}. © 2022 Walter de Gruyter GmbH, Berlin/Boston. | * |
dc.language | English | * |
dc.publisher | De Gruyter Open Ltd | * |
dc.title | Isomorphisms among quantum Grothendieck rings and propagation of positivity | * |
dc.type | Article | * |
dc.relation.issue | 785 | * |
dc.relation.volume | 2022 | * |
dc.relation.index | SCIE | * |
dc.relation.index | SCOPUS | * |
dc.relation.startpage | 117 | * |
dc.relation.lastpage | 185 | * |
dc.relation.journaltitle | Journal fur die Reine und Angewandte Mathematik | * |
dc.identifier.doi | 10.1515/crelle-2021-0088 | * |
dc.identifier.wosid | WOS:000755032600001 | * |
dc.identifier.scopusid | 2-s2.0-85124826960 | * |
dc.author.google | Fujita R. | * |
dc.author.google | Hernandez D. | * |
dc.author.google | Oh S.-J. | * |
dc.author.google | Oya H. | * |
dc.contributor.scopusid | 오세진(55636183200) | * |
dc.date.modifydate | 20240222164805 | * |