Pieri Formulae and Specialisation of Super Jacobi Polynomials
We give a new proof of the fact that the Euler supercharacters of the Lie superalgebra osp(2m + 1, 2n) can be obtained as a certain limit of the super Jacobi polynomials. The known proof was not direct one and it was mostly based on calculations. In this paper we propose more simple and more concept...
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Saratov State University
2019-12-01
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doaj-831412df6e34461db1b9a1f8c69ac2e72020-12-01T10:07:36ZengSaratov State UniversityИзвестия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика1816-97912541-90052019-12-0119437738810.18500/1816-9791-2019-19-4-377-388Pieri Formulae and Specialisation of Super Jacobi PolynomialsSergeev, Alexander Nikolaevich0Zharinov, Egor D.1Saratov State University, Russia, 410026, Saratov, Astrahanskaya str., 83Saratov State University, Russia, 410026, Saratov, Astrahanskaya str., 83We give a new proof of the fact that the Euler supercharacters of the Lie superalgebra osp(2m + 1, 2n) can be obtained as a certain limit of the super Jacobi polynomials. The known proof was not direct one and it was mostly based on calculations. In this paper we propose more simple and more conceptional proof. The main idea is to use the Pieri formulae from the beginning. It turns out that the super Jacobi polynomials and their specialisations can be uniquely characterised by two properties. The first one is that they are eigenfunctions of CMS operator and the second one is that they satisfy the Pieri formulae. As by product we get some interesting identities involving a Young diagram and rational functions. We hope that our approach can be useful in many similar cases.https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2020/04/377-388sergeev-zharinov_5.pdfquantum cms operatorpieri formulasuper jacobi polynomialsuperalgebraeuler supercharacter |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Sergeev, Alexander Nikolaevich Zharinov, Egor D. |
spellingShingle |
Sergeev, Alexander Nikolaevich Zharinov, Egor D. Pieri Formulae and Specialisation of Super Jacobi Polynomials Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика quantum cms operator pieri formula super jacobi polynomial superalgebra euler supercharacter |
author_facet |
Sergeev, Alexander Nikolaevich Zharinov, Egor D. |
author_sort |
Sergeev, Alexander Nikolaevich |
title |
Pieri Formulae and Specialisation of Super Jacobi Polynomials |
title_short |
Pieri Formulae and Specialisation of Super Jacobi Polynomials |
title_full |
Pieri Formulae and Specialisation of Super Jacobi Polynomials |
title_fullStr |
Pieri Formulae and Specialisation of Super Jacobi Polynomials |
title_full_unstemmed |
Pieri Formulae and Specialisation of Super Jacobi Polynomials |
title_sort |
pieri formulae and specialisation of super jacobi polynomials |
publisher |
Saratov State University |
series |
Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
issn |
1816-9791 2541-9005 |
publishDate |
2019-12-01 |
description |
We give a new proof of the fact that the Euler supercharacters of the Lie superalgebra osp(2m + 1, 2n) can be obtained as a certain limit of the super Jacobi polynomials. The known proof was not direct one and it was mostly based on calculations. In this paper we propose more simple and more conceptional proof. The main idea is to use the Pieri formulae from the beginning. It turns out that the super Jacobi polynomials and their specialisations can be uniquely characterised by two properties. The first one is that they are eigenfunctions of CMS operator and the second one is that they satisfy the Pieri formulae. As by product we get some interesting identities involving a Young diagram and rational functions. We hope that our approach can be useful in many similar cases. |
topic |
quantum cms operator pieri formula super jacobi polynomial superalgebra euler supercharacter |
url |
https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2020/04/377-388sergeev-zharinov_5.pdf |
work_keys_str_mv |
AT sergeevalexandernikolaevich pieriformulaeandspecialisationofsuperjacobipolynomials AT zharinovegord pieriformulaeandspecialisationofsuperjacobipolynomials |
_version_ |
1724411086352941056 |