The orthogonal weingarten formula in compact form

Letters in Mathematical Physics

Volumn 91, Issue 2, 2010, Pages 105-118

  Banica, Teodor ^a  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

Author keywords

Orthogonal group; Weingarten function

Indexed keywords

EID: 77949773791     PISSN: 03779017     EISSN: 15730530     Source Type: Journal    
DOI: 10.1007/s11005-009-0363-y     Document Type: Article

References (13)

1. Banica T., Collins B.: Integration over compact quantum groups. Publ. Res. Inst. Math. Sci. 43, 277-302 (2007).
2. Banica, T., Collins, B., Schlenker, J.-M.: On orthogonal matrices maximizing the 1-norm. arxiv: 0901. 2923.
3. Banica, T., Collins, B., Schlenker, J.-M.: On polynomial integrals over the orthogonal group. arxiv: 0910. 1258.
4. Banica, T., Curran, S.: Gram determinants and generalized Weingarten functions (in preparation).
5. Brauer R.: On algebras which are connected with the semisimple continuous groups. Ann. Math. 38, 857-872 (1937).
6. Collins B.: Moments and cumulants of polynomial random variables on unitary groups, the Itzykson-Zuber integral, and free probability. Int. Math. Res. Not. 17, 953-982 (2003).
7. Collins, B., Matsumoto, S.: On some properties of orthogonal Weingarten functions. J. Math. Phys. (2009, in press).
8. Collins B., Śniady P.: Integration with respect to the Haar measure on the unitary, orthogonal and symplectic group. Comm. Math. Phys. 264, 773-795 (2006).
9. Curran S.: Quantum exchangeable sequences of algebras. Indiana Univ. Math. J. 58, 1097-1126 (2009).
10. Di Francesco P.: Meander determinants. Comm. Math. Phys. 191, 543-583 (1998).
11. Matsumoto, S., Novak, J.: Symmetric polynomials in Jucys-Murphy elements and the Weingarten function. arxiv: 0905. 1992.
12. Weingarten D.: Asymptotic behavior of group integrals in the limit of infinite rank. J. Math. Phys. 19, 999-1001 (1978).
13. Zinn-Justin, P.: Jucys-Murphy elements and Weingarten matrices. Lett. Math. Phys. 91 (2010). doi: 10. 1007/s11005-009-0365-9.