Singular Nonsymmetric Macdonald Polynomials and Quasistaircases
Singular nonsymmetric Macdonald polynomials are constructed by use of the representation theory of the Hecke algebras of the symmetric groups. These polynomials are labeled by quasistaircase partitions and are associated with special parameter values (q,t). For N variables, there are singular polyno...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210600 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Singular Nonsymmetric Macdonald Polynomials and Quasistaircases. Laura Colmenarejo and Charles F. Dunkl. SIGMA 16 (2020), 010, 27 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862743084900548608 |
|---|---|
| author | Colmenarejo, Laura Dunkl, Charles F. |
| author_facet | Colmenarejo, Laura Dunkl, Charles F. |
| citation_txt | Singular Nonsymmetric Macdonald Polynomials and Quasistaircases. Laura Colmenarejo and Charles F. Dunkl. SIGMA 16 (2020), 010, 27 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Singular nonsymmetric Macdonald polynomials are constructed by use of the representation theory of the Hecke algebras of the symmetric groups. These polynomials are labeled by quasistaircase partitions and are associated with special parameter values (q,t). For N variables, there are singular polynomials for any pair of positive integers m and n, with 2 ≤ n ≤ N, and parameter values (q,t) satisfying qᵃtᵇ = 1 exactly when a = rm and b = rn, for some integer r. The coefficients of nonsymmetric Macdonald polynomials with respect to the basis of monomials {xᵅ} are rational functions of q and t. In this paper, we present the construction of subspaces of singular nonsymmetric Macdonald polynomials specialized to particular values of (q,t). The key part of this construction is to show that the coefficients have no poles at the special values of (q,t). Moreover, this subspace of singular Macdonald polynomials for the special values of the parameters is an irreducible module for the Hecke algebra of type AN₋₁.
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| first_indexed | 2025-12-17T12:04:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210600 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:04:19Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Colmenarejo, Laura Dunkl, Charles F. 2025-12-12T10:37:05Z 2020 Singular Nonsymmetric Macdonald Polynomials and Quasistaircases. Laura Colmenarejo and Charles F. Dunkl. SIGMA 16 (2020), 010, 27 pages 1815-0659 2020 Mathematics Subject Classification: 33D52; 20C08; 33D80; 05E10 arXiv:1909.00071 https://nasplib.isofts.kiev.ua/handle/123456789/210600 https://doi.org/10.3842/SIGMA.2020.010 Singular nonsymmetric Macdonald polynomials are constructed by use of the representation theory of the Hecke algebras of the symmetric groups. These polynomials are labeled by quasistaircase partitions and are associated with special parameter values (q,t). For N variables, there are singular polynomials for any pair of positive integers m and n, with 2 ≤ n ≤ N, and parameter values (q,t) satisfying qᵃtᵇ = 1 exactly when a = rm and b = rn, for some integer r. The coefficients of nonsymmetric Macdonald polynomials with respect to the basis of monomials {xᵅ} are rational functions of q and t. In this paper, we present the construction of subspaces of singular nonsymmetric Macdonald polynomials specialized to particular values of (q,t). The key part of this construction is to show that the coefficients have no poles at the special values of (q,t). Moreover, this subspace of singular Macdonald polynomials for the special values of the parameters is an irreducible module for the Hecke algebra of type AN₋₁. The authors would like to thank Jean-Gabriel Luque for his fruitful discussions and his collaboration during the previous years. They also thank the referees for their careful reading and suggestions on improving the presentation. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Singular Nonsymmetric Macdonald Polynomials and Quasistaircases Article published earlier |
| spellingShingle | Singular Nonsymmetric Macdonald Polynomials and Quasistaircases Colmenarejo, Laura Dunkl, Charles F. |
| title | Singular Nonsymmetric Macdonald Polynomials and Quasistaircases |
| title_full | Singular Nonsymmetric Macdonald Polynomials and Quasistaircases |
| title_fullStr | Singular Nonsymmetric Macdonald Polynomials and Quasistaircases |
| title_full_unstemmed | Singular Nonsymmetric Macdonald Polynomials and Quasistaircases |
| title_short | Singular Nonsymmetric Macdonald Polynomials and Quasistaircases |
| title_sort | singular nonsymmetric macdonald polynomials and quasistaircases |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210600 |
| work_keys_str_mv | AT colmenarejolaura singularnonsymmetricmacdonaldpolynomialsandquasistaircases AT dunklcharlesf singularnonsymmetricmacdonaldpolynomialsandquasistaircases |