Pieri integral formula and asymptotics of Jack unitary characters
We introduce Jack (unitary) characters and prove two kinds of formulas that are suitable for their asymptotics, as the lengths of the signatures that parametrize them go to infinity. The first kind includes several integral representations for Jack characters of one variable. The second identity we...
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| Format: | Article |
| Language: | English |
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Springer International Publishing
2018
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| Online Access: | http://hdl.handle.net/1721.1/116960 |
| _version_ | 1826194024884600832 |
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| author | Cuenca, Cesar |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Cuenca, Cesar |
| author_sort | Cuenca, Cesar |
| collection | MIT |
| description | We introduce Jack (unitary) characters and prove two kinds of formulas that are suitable for their asymptotics, as the lengths of the signatures that parametrize them go to infinity. The first kind includes several integral representations for Jack characters of one variable. The second identity we prove is the Pieri integral formula for Jack characters which, in a sense, is dual to the well known Pieri rule for Jack polynomials. The Pieri integral formula can also be seen as a functional equation for irreducible spherical functions of virtual Gelfand pairs. As an application of our formulas, we study the asymptotics of Jack characters as the corresponding signatures grow to infinity in the sense of Vershik–Kerov. We prove the existence of a small δ>0 such that the Jack characters of m variables have a uniform limit on the δ -neighborhood of the m-dimensional torus. Our result specializes to a theorem of Okounkov and Olshanski. |
| first_indexed | 2024-09-23T09:49:20Z |
| format | Article |
| id | mit-1721.1/116960 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:49:20Z |
| publishDate | 2018 |
| publisher | Springer International Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1169602022-09-26T13:56:54Z Pieri integral formula and asymptotics of Jack unitary characters Cuenca, Cesar Massachusetts Institute of Technology. Department of Mathematics Cuenca, Cesar We introduce Jack (unitary) characters and prove two kinds of formulas that are suitable for their asymptotics, as the lengths of the signatures that parametrize them go to infinity. The first kind includes several integral representations for Jack characters of one variable. The second identity we prove is the Pieri integral formula for Jack characters which, in a sense, is dual to the well known Pieri rule for Jack polynomials. The Pieri integral formula can also be seen as a functional equation for irreducible spherical functions of virtual Gelfand pairs. As an application of our formulas, we study the asymptotics of Jack characters as the corresponding signatures grow to infinity in the sense of Vershik–Kerov. We prove the existence of a small δ>0 such that the Jack characters of m variables have a uniform limit on the δ -neighborhood of the m-dimensional torus. Our result specializes to a theorem of Okounkov and Olshanski. 2018-07-12T20:23:42Z 2018-09-02T05:00:05Z 2017-11 2018-06-21T04:06:22Z Article http://purl.org/eprint/type/JournalArticle 1022-1824 1420-9020 http://hdl.handle.net/1721.1/116960 Cuenca, Cesar. “Pieri Integral Formula and Asymptotics of Jack Unitary Characters.” Selecta Mathematica, vol. 24, no. 3, July 2018, pp. 2737–89. en https://doi.org/10.1007/s00029-017-0373-z Selecta Mathematica Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer International Publishing AG, part of Springer Nature application/pdf Springer International Publishing Springer International Publishing |
| spellingShingle | Cuenca, Cesar Pieri integral formula and asymptotics of Jack unitary characters |
| title | Pieri integral formula and asymptotics of Jack unitary characters |
| title_full | Pieri integral formula and asymptotics of Jack unitary characters |
| title_fullStr | Pieri integral formula and asymptotics of Jack unitary characters |
| title_full_unstemmed | Pieri integral formula and asymptotics of Jack unitary characters |
| title_short | Pieri integral formula and asymptotics of Jack unitary characters |
| title_sort | pieri integral formula and asymptotics of jack unitary characters |
| url | http://hdl.handle.net/1721.1/116960 |
| work_keys_str_mv | AT cuencacesar pieriintegralformulaandasymptoticsofjackunitarycharacters |