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...

Full description

Saved in:
Bibliographic Details
Published in:Algebras and representation theory Vol. 27; no. 1; pp. 583 - 611
Main Authors: Lee, Kyu-Hwan, Oh, Se-Jin
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.02.2024
Springer Nature B.V
Subjects:
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
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-023-10225-x