nLab seminormal representation

Idea

(…)

Related concepts

• regular representation

• representation theory of the symmetric group

• Jucys-Murphy element

• Gelfand-Tsetlin basis

References

Due to:

• Alfred Young, On quantitative substitutional analysis VI, Proc. London Math. Soc. (2) 31 (1931), 253-289. Reprinted in: The Collected Papers of Alfred Young, 1873-1940, Mathematical Expositions 21, Univ. of Toronto Press, Toronto and Buffalo, 1977

Further discussion in the context of Jucys-Murphy elements:

• G. E. Murphy, A new construction of Young’s seminormal representation of the symmetric groups, Journal of Algebra Volume 69, Issue 2, April 1981, Pages 287-297 (doi:10.1016/0021-8693(81)90205-2)

• G. E. Murphy, The idempotents of the symmetric group and Nakayama’s conjecture, Journal of Algebra Volume 81, Issue 1, March 1983, Pages 258-265 (pdf)

• G. E. Murphy, On the representation theory of the symmetric groups and associated Hecke algebras, J. Algebra 152 (1992) 492–513 (pdf, doi:10.1016/0021-8693(92)90045-N))

On the representation theory of the symmetric group via the Gelfand-Tsetlin basis/seminormal representation:

• Anatoly Vershik, Andrei Okounkov, A New Approach to the Representation Theory of the Symmetric Groups,

  Part I: Selecta Mathematica, New Series 2, 581-605 (arXiv:math/0503040, doi:10.1007/BF02433451); Part II (incorporates Part I in revised and improved form): Russian version: Записки научных семинаров ПОМИ 307 (2004), 57–98 (Zapiski nauchnyh seminarov POMI 307 (2004), 57–98); English version: Journal of Mathematical Sciences 131 (2005), 5471–5494 (doi:10.1007/s10958-005-0421-7).