We give formulae relating the value Xλ (g) of an irreducible character of a classical group G to entries of powers of the matrix g ε G. This yields a far-reaching generalization of a result of J.L. Cisneros-Molina concerning the GL 2 case [1].
@article{bwmeta1.element.doi-10_2478_s11533-006-0004-y,
author = {P\'eter Frenkel},
title = {Character formulae for classical groups},
journal = {Open Mathematics},
volume = {4},
year = {2006},
pages = {242-249},
zbl = {1101.20026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-006-0004-y}
}
Péter Frenkel. Character formulae for classical groups. Open Mathematics, Tome 4 (2006) pp. 242-249. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-006-0004-y/
[1] J. L. Cisneros-Molina: “An invariant of 2 × 2 matrices”, Electr. J. Linear Algebra, Vol. 13, (2005), pp. 146–152. | Zbl 1104.15023
[2] W. Fulton and J. Harris: Representation theory, GTM, Springer, New York, 1991.
[3] R. Goodman and N.R. Wallach: Representations and invariants of the classical groups, Cambridge University Press, Cambridge, 1998. | Zbl 0901.22001
[4] H. Weyl: “Theorie der Darstellung kontinuerlicher halbeinfacher Gruppen durch lineare Transformationen, I, II, III, und Nachtrag”, Math. Zeitschrift, Vol. 23, (1925), pp. 271–309; Vol. 24, (1925), pp. 328–376, 377–395, 789–791; reprinted in Selecta Hermann Weyl, Birkhäuser, Basel, 1956, pp. 262–366 http://dx.doi.org/10.1007/BF01506234
[5] H. Weyl: The classical groups, Their invariants and representations, Princeton University Press, Princeton, 1946.