Abstract
Let G be a finite group. A complete system of pairwise orthogonal idempotents is constructed for the wreath product of G by the symmetric group by means of a fusion procedure, that is by consecutive evaluations of a rational function with values in the group ring. This complete system of idempotents is indexed by standard Young multi-tableaux. Associated to the wreath product of G by the symmetric group, a Baxterized form for the Artin generators of the symmetric group is defined and appears in the rational function used in the fusion procedure.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cherednik, I.: On special bases of irreducible finite-dimensional representations of the degenerate affine Hecke algebra. Funct. Anal. Appl. 20, 87–89 (1986)
Cherednik, I.: Computation of monodromy of certain W-invariant local systems of types B, C, and D. Funct. Anal. Appl. 24, 78–79 (1990)
Isaev, A., Molev, A.: Fusion procedure for the Brauer algebra. Algebra Anal. 22(3), 142–154 (2010). arXiv:0812.4113
Isaev, A., Molev, A., Ogievetsky, O.: A new fusion procedure for the Brauer algebra and evaluation homomorphisms. Int. Math. Res. Not. 2012(11), 2571–2606 (2012)
Isaev, A., Molev, A., Ogievetsky, O.: Idempotents for Birman–Murakami–Wenzl algebras and reflection equation. arXiv:1111.2502 (2011)
Isaev, A., Molev, A., Os’kinm A.: On the idempotents of Hecke algebras. Lett. Math. Phys. 85, 79–90 (2008). arXiv:0804.4214
Isaev, A., Ogievetsky, O.: On Baxterized solutions of reflection equation and integrable chain models. Nucl. Phys. B760, 167–183 (2007). arXiv:math-ph/0510078
James, G., Kerber, A.: The Representation Theory of the Symmetric Group. Addison-Wesley, Reading, MA (1981)
Jucys, A.: On the Young operators of the symmetric group. Liet. Fiz. Rink. 6, 163–180 (1966)
Jucys, A.: Factorization of Young projection operators for the symmetric group. Liet. Fiz. Rink. 11, 5–10 (1971)
Macdonald, I.: Symmetric Functions and Hall Polynomials. Clarendon Press, Oxford (1998)
Molev, A.: On the fusion procedure for the symmetric group. Rep. Math. Phys. 61, 181–188 (2008). arXiv:math/0612207
Murphy, G.: A new construction of Young’s seminormal representation of the symmetric group. J. Algebra 69, 287–291 (1981)
Nazarov, M.: Yangians and Capelli identities. In: Olshanski, G.I. (ed.) Kirillov’s Seminar on Representation. Theory Amer. Math. Soc. Transl., vol. 181, pp. 139–163. Amer. Math. Soc. Providence, RI (1998)
Nazarov, M.: Mixed hook-length formula for degenerate affine Hecke algebras. Lect. Notes Math. 1815, 223–236 (2003)
Nazarov, M.: A mixed hook-length formula for affine Hecke algebras. Eur. J. Comb. 25, 1345–1376 (2004)
Ogievetsky, O., Poulain d’Andecy, L.: Fusion formula for Coxeter groups of type B and complex reflection groups G(m,1,n). arXiv:1111.6293 (2011)
Ogievetsky, O., Poulain d’Andecy, L.: Fusion formula for cyclotomic Hecke algebras. arXiv:1301.4237 (2013)
Pushkarev, I.A.: On the representation theory of wreath products of finite groups and symmetric groups. J. Math. Sci. 96, 3590–3599 (1999)
Wang, W.: Vertex algebras and the class algebras of wreath products. Proc. Lond. Math. Soc. 88, 381–404 (2004). arXiv:math/0203004
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Poulain d’Andecy, L. Fusion Procedure for Wreath Products of Finite Groups by the Symmetric Group. Algebr Represent Theor 17, 809–830 (2014). https://doi.org/10.1007/s10468-013-9419-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10468-013-9419-x