Character formulae for classical groups

• Autorzy: Péter Frenkel
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

Character formula; irreducible character; classical group; powers of a matrix; 20G05

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2006
• Tom: 4
• Numer: 2
• Strony: 242-249

Daty

wydano

2006-06-01

online

2006-06-01

Twórcy

autor

Péter Frenkel

• Budapest University of Technology and Economics,

Bibliografia

• [1] J. L. Cisneros-Molina: “An invariant of 2 × 2 matrices”, Electr. J. Linear Algebra, Vol. 13, (2005), pp. 146–152.
• [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.
• [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.

Identyfikatory

DOI

10.2478/s11533-006-0004-y