Free probability on Hecke algebras and certain group C^{*}-algebras induced by Hecke algebras
In this paper, by establishing free-probabilistic models on the Hecke algebras \(\mathcal{H}\left(GL_{2}(\mathbb{Q}_{p})\right)\) induced by \(p\)-adic number fields \(\mathbb{Q}_{p}\), we construct free probability spaces for all primes \(p\). Hilbert-space representations are induced by such free-...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2016-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol36/2/art/opuscula_math_3609.pdf |
| _version_ | 1818586274664022016 |
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| author | Ilwoo Cho |
| author_facet | Ilwoo Cho |
| author_sort | Ilwoo Cho |
| collection | DOAJ |
| description | In this paper, by establishing free-probabilistic models on the Hecke algebras \(\mathcal{H}\left(GL_{2}(\mathbb{Q}_{p})\right)\) induced by \(p\)-adic number fields \(\mathbb{Q}_{p}\), we construct free probability spaces for all primes \(p\). Hilbert-space representations are induced by such free-probabilistic structures. We study \(C^{*}\)-algebras induced by certain partial isometries realized under the representations. |
| first_indexed | 2024-12-16T08:50:22Z |
| format | Article |
| id | doaj.art-14e46b5d74274cd6854d43254d41df32 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-16T08:50:22Z |
| publishDate | 2016-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-14e46b5d74274cd6854d43254d41df322022-12-21T22:37:28ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742016-01-01362153187http://dx.doi.org/10.7494/OpMath.2016.36.2.1533609Free probability on Hecke algebras and certain group C^{*}-algebras induced by Hecke algebrasIlwoo Cho0St. Ambrose University, Department of Mathematics, 421 Ambrose Hall, 518 W. Locust St., Davenport, Iowa, 52803, USAIn this paper, by establishing free-probabilistic models on the Hecke algebras \(\mathcal{H}\left(GL_{2}(\mathbb{Q}_{p})\right)\) induced by \(p\)-adic number fields \(\mathbb{Q}_{p}\), we construct free probability spaces for all primes \(p\). Hilbert-space representations are induced by such free-probabilistic structures. We study \(C^{*}\)-algebras induced by certain partial isometries realized under the representations.http://www.opuscula.agh.edu.pl/vol36/2/art/opuscula_math_3609.pdffree probabilityfree momentsfree cumulantsHecke algebrasnormal Hecke subalgebrasrepresentationsgroupsgroup \(C^{*}\)-algebras |
| spellingShingle | Ilwoo Cho Free probability on Hecke algebras and certain group C^{*}-algebras induced by Hecke algebras Opuscula Mathematica free probability free moments free cumulants Hecke algebras normal Hecke subalgebras representations groups group \(C^{*}\)-algebras |
| title | Free probability on Hecke algebras and certain group C^{*}-algebras induced by Hecke algebras |
| title_full | Free probability on Hecke algebras and certain group C^{*}-algebras induced by Hecke algebras |
| title_fullStr | Free probability on Hecke algebras and certain group C^{*}-algebras induced by Hecke algebras |
| title_full_unstemmed | Free probability on Hecke algebras and certain group C^{*}-algebras induced by Hecke algebras |
| title_short | Free probability on Hecke algebras and certain group C^{*}-algebras induced by Hecke algebras |
| title_sort | free probability on hecke algebras and certain group c algebras induced by hecke algebras |
| topic | free probability free moments free cumulants Hecke algebras normal Hecke subalgebras representations groups group \(C^{*}\)-algebras |
| url | http://www.opuscula.agh.edu.pl/vol36/2/art/opuscula_math_3609.pdf |
| work_keys_str_mv | AT ilwoocho freeprobabilityonheckealgebrasandcertaingroupcalgebrasinducedbyheckealgebras |