Cluster Variables on Certain Double Bruhat Cells of Type (u,e) and Monomial Realizations of Crystal Bases of Type A
Let G be a simply connected simple algebraic group over C, B and B− be two opposite Borel subgroups in G and W be the Weyl group. For u, v∈W, it is known that the coordinate ring C[Gu,v] of the double Bruhat cell Gu,v=BuB∩B−vB− is isomorphic to an upper cluster algebra A¯(i)C and the generalized min...
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| Дата: | 2015 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2015
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147010 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Cluster Variables on Certain Double Bruhat Cells of Type (u,e) and Monomial Realizations of Crystal Bases of Type A / Y. Kanakubo, T. Nakashima // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 11 назв. — англ. |
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irk-123456789-1470102019-02-13T01:24:47Z Cluster Variables on Certain Double Bruhat Cells of Type (u,e) and Monomial Realizations of Crystal Bases of Type A Kanakubo, Y. Nakashima, T. Let G be a simply connected simple algebraic group over C, B and B− be two opposite Borel subgroups in G and W be the Weyl group. For u, v∈W, it is known that the coordinate ring C[Gu,v] of the double Bruhat cell Gu,v=BuB∩B−vB− is isomorphic to an upper cluster algebra A¯(i)C and the generalized minors {Δ(k;i)} are the cluster variables belonging to a given initial seed in C[Gu,v] [Berenstein A., Fomin S., Zelevinsky A., Duke Math. J. 126 (2005), 1-52]. In the case G=SLr₊₁(C), v=e and some special u∈W, we shall describe the generalized minors {Δ(k;i)} as summations of monomial realizations of certain Demazure crystals. 2015 Article Cluster Variables on Certain Double Bruhat Cells of Type (u,e) and Monomial Realizations of Crystal Bases of Type A / Y. Kanakubo, T. Nakashima // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 11 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 13F60; 81R50; 17B37 DOI:10.3842/SIGMA.2015.033 http://dspace.nbuv.gov.ua/handle/123456789/147010 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Let G be a simply connected simple algebraic group over C, B and B− be two opposite Borel subgroups in G and W be the Weyl group. For u, v∈W, it is known that the coordinate ring C[Gu,v] of the double Bruhat cell Gu,v=BuB∩B−vB− is isomorphic to an upper cluster algebra A¯(i)C and the generalized minors {Δ(k;i)} are the cluster variables belonging to a given initial seed in C[Gu,v] [Berenstein A., Fomin S., Zelevinsky A., Duke Math. J. 126 (2005), 1-52]. In the case G=SLr₊₁(C), v=e and some special u∈W, we shall describe the generalized minors {Δ(k;i)} as summations of monomial realizations of certain Demazure crystals. |
| format |
Article |
| author |
Kanakubo, Y. Nakashima, T. |
| spellingShingle |
Kanakubo, Y. Nakashima, T. Cluster Variables on Certain Double Bruhat Cells of Type (u,e) and Monomial Realizations of Crystal Bases of Type A Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Kanakubo, Y. Nakashima, T. |
| author_sort |
Kanakubo, Y. |
| title |
Cluster Variables on Certain Double Bruhat Cells of Type (u,e) and Monomial Realizations of Crystal Bases of Type A |
| title_short |
Cluster Variables on Certain Double Bruhat Cells of Type (u,e) and Monomial Realizations of Crystal Bases of Type A |
| title_full |
Cluster Variables on Certain Double Bruhat Cells of Type (u,e) and Monomial Realizations of Crystal Bases of Type A |
| title_fullStr |
Cluster Variables on Certain Double Bruhat Cells of Type (u,e) and Monomial Realizations of Crystal Bases of Type A |
| title_full_unstemmed |
Cluster Variables on Certain Double Bruhat Cells of Type (u,e) and Monomial Realizations of Crystal Bases of Type A |
| title_sort |
cluster variables on certain double bruhat cells of type (u,e) and monomial realizations of crystal bases of type a |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147010 |
| citation_txt |
Cluster Variables on Certain Double Bruhat Cells of Type (u,e) and Monomial Realizations of Crystal Bases of Type A / Y. Kanakubo, T. Nakashima // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 11 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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