Auto-Correlation Functions for Unitary Groups

We compute the auto-correlations functions of order m ≥ 1 for the characteristic polynomials of random matrices from certain subgroups of the unitary groups U ( 2 ) and U ( 3 ) by establishing new branching rules. These subgroups can be understood as certain analogues of Sato–Tate groups of USp ( 4...

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Veröffentlicht in:	Algebras and representation theory Jg. 27; H. 1; S. 583 - 611
Hauptverfasser:	Lee, Kyu-Hwan, Oh, Se-Jin
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Dordrecht Springer Netherlands 01.02.2024 Springer Nature B.V
Schlagworte:	Algebra Associative Rings and Algebras Autocorrelation functions Combinatorics Commutative Rings and Algebras Identities Mathematics Mathematics and Statistics Non-associative Rings and Algebras Polynomials Subgroups 05E05 11M50 Auto-correlation functions Symmetric functions 17B10 Unitary groups
ISSN:	1386-923X, 1572-9079
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Abstract	We compute the auto-correlations functions of order m ≥ 1 for the characteristic polynomials of random matrices from certain subgroups of the unitary groups U ( 2 ) and U ( 3 ) by establishing new branching rules. These subgroups can be understood as certain analogues of Sato–Tate groups of USp ( 4 ) in our previous paper. Our computation yields symmetric polynomial identities with m -variables involving irreducible characters of U ( m ) for all m ≥ 1 in an explicit, uniform way.
AbstractList	We compute the auto-correlations functions of order m≥1 for the characteristic polynomials of random matrices from certain subgroups of the unitary groups U(2) and U(3) by establishing new branching rules. These subgroups can be understood as certain analogues of Sato–Tate groups of USp(4) in our previous paper. Our computation yields symmetric polynomial identities with m-variables involving irreducible characters of U(m) for all m≥1 in an explicit, uniform way. We compute the auto-correlations functions of order m ≥ 1 for the characteristic polynomials of random matrices from certain subgroups of the unitary groups U ( 2 ) and U ( 3 ) by establishing new branching rules. These subgroups can be understood as certain analogues of Sato–Tate groups of USp ( 4 ) in our previous paper. Our computation yields symmetric polynomial identities with m -variables involving irreducible characters of U ( m ) for all m ≥ 1 in an explicit, uniform way.
Author	Oh, Se-Jin Lee, Kyu-Hwan
Author_xml	– sequence: 1 givenname: Kyu-Hwan surname: Lee fullname: Lee, Kyu-Hwan organization: Department of Mathematics, University of Connecticut – sequence: 2 givenname: Se-Jin surname: Oh fullname: Oh, Se-Jin email: sejin092@gmail.com organization: Department of Mathematics, Sungkyunkwan University
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Cites_doi	10.1007/s10240-008-0015-2 10.1090/conm/487/09529 10.1007/s002200000262 10.1007/s00220-003-0852-2 10.1007/s002200100547 10.1007/s002200000256 10.1007/s00220-006-1503-1 10.1002/cpa.20092 10.1016/S0550-3213(02)00185-2 10.4310/CNTP.2008.v2.n3.a4 10.1007/s002200000261 10.1088/0305-4470/22/21/015 10.1088/0305-4470/21/22/014 10.1103/PhysRevLett.75.2304 10.1016/S0550-3213(02)00904-5 10.1088/0305-4470/19/17/016 10.1088/0305-4470/34/22/304 10.1112/S0010437X12000279 10.1090/pspum/055.1/1265537 10.1016/j.aim.2022.108309 10.1112/S0024611504015175 10.1007/s10240-008-0016-1 10.4007/annals.2010.171.779 10.1090/ulect/012 10.1090/coll/045 10.1007/978-1-4614-8024-2
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Snippet	We compute the auto-correlations functions of order m ≥ 1 for the characteristic polynomials of random matrices from certain subgroups of the unitary groups U... We compute the auto-correlations functions of order m≥1 for the characteristic polynomials of random matrices from certain subgroups of the unitary groups U(2)...
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SubjectTerms	Algebra Associative Rings and Algebras Autocorrelation functions Combinatorics Commutative Rings and Algebras Identities Mathematics Mathematics and Statistics Non-associative Rings and Algebras Polynomials Subgroups
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Title	Auto-Correlation Functions for Unitary Groups
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