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: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
01.02.2024
Springer Nature B.V |
| Schlagworte: | |
| ISSN: | 1386-923X, 1572-9079 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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. |
|---|---|
| Bibliographie: | 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 |