Combinatorial aspects of orthogonal group integrals

International Journal of Mathematics

Volumn 22, Issue 11, 2011, Pages 1611-1646

  Banica, Teodor ^a   Schlenker, Jean Marc ^b  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

^b INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

Haar measure; Orthogonal group; Weingarten function

Indexed keywords

EID: 82955194570     PISSN: 0129167X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129167X11007343     Document Type: Article

References (22)

1. T. Banica, The orthogonal Weingarten formula in compact form, Lett. Math. Phys. 91 (2010) 105-118.
2. T. Banica, B. Collins and J.-M. Schlenker, On orthogonal matrices maximizing the 1-norm, Indiana Univ. Math. J. 59 (2010) 839-856.
3. T. Banica, B. Collins and J.-M. Schlenker, On polynomial integrals over the orthogonal group, J. Combin. Theory Ser. A 118 (2011) 778-795.
4. T. Banica and S. Curran, Decomposition results for Gram matrix determinants, J. Math. Phys. 51 (2010) 1-14.
5. T. Banica, S. Curran and R. Speicher, De Finetti theorems for easy quantum groups, to appear in Ann. Probab.
6. T. Banica, S. Curran and R. Speicher, Stochastic aspects of easy quantum groups, Probab. Theory Related Fields 149 (2011) 435-462.
7. R. Brauer, On algebras which are connected with the semisimple continuous groups, Ann. of Math. 38 (1937) 857-872.
8. B. Collins, Moments and cumulants of polynomial random variables on unitary groups, the Itzykson-Zuber integral, and free probability, Int. Math. Res. Not. 17 (2003) 953-982. (Pubitemid 36598539)
9. B. Collins, A. Guionnet and E. Maurel-Segala, Asymptotics of unitary and orthogonal matrix integrals, Adv. Math. 222 (2009) 172-215.
10. B. Collins and S. Matsumoto, On some properties of orthogonal Weingarten functions, J. Math. Phys. 50 (2009) 1-18.
11. B. Collins and P. Sniady, Integration with respect to the Haar measure on the unitary, orthogonal and symplectic group, Comm. Math. Phys. 264 (2006) 773-795. (Pubitemid 43707576)
12. B. Collins and P. Sniady, Representation of Lie groups and random matrices, Trans. Amer. Math. Soc. 361 (2009) 3269-3287.
13. P. Diaconis and M. Shahshahani, On the eigenvalues of random matrices, J. Applied Probab. 31 (1994) 49-62. (Pubitemid 126040789)
14. P. Di Francesco, Meander determinants, Comm. Math. Phys. 191 (1998) 543-583. (Pubitemid 128360194)
15. P. Di Francesco, O. Golinelli and E. Guitter, Meanders and the Temperley-Lieb algebra, Comm. Math. Phys. 186 (1997) 1-59. (Pubitemid 127353869)
16. S. Matsumoto and J. Novak, Primitive factorizations, Jucys-Murphy elements, and matrix models, preprint (2010), arXiv:1005.0151.
17. Y. A. Neretin, Hua type integrals over unitary groups and over projective limits of unitary groups, Duke Math. J. 114 (2002) 239-266.
18. J. Novak, Jucys-Murphy elements and the unitary Weingarten function, Banach Cent. Publ. 89 (2010) 231-235.
19. G. I. Olshanskii, Unitary representations of infinite-dimensional pairs (G,K) and the formalism of R. Howe, Adv. Stud. Contemp. Math. 7 (1990) 269-463.
20. D. Petz and J. Réffy, Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices, Probab. Theory Relat. Fields 133 (2005) 175-189. (Pubitemid 41274555)
21. D. Weingarten, Asymptotic behavior of group integrals in the limit of infinite rank, J. Math. Phys. 19 (1978) 999-1001.
22. P. Zinn-Justin, Jucys-Murphy elements and Weingarten matrices, Lett. Math. Phys. 91 (2010) 119-127.