2

In most textbooks, I have seen material on representation theory of the orthogonal group and its Lie algebra, and at most of the Lorentz group. However, I haven't seen any references talking about the representation theory of the general indefinite orthogonal group and its Lie algebra. Are there any such references at all?

Ishan Deo
  • 3,886
  • 3
    https://math.stackexchange.com/questions/3234729/representation-theory-of-sop-q – Eric Towers Nov 08 '21 at 05:37
  • 3
    https://math.stackexchange.com/questions/139110/what-is-the-lie-algebra-of-the-indefinite-orthogonal-group – Eric Towers Nov 08 '21 at 05:38
  • Basic Algebra By：Anthony W. Knapp – C.F.G Nov 08 '21 at 06:53
  • 1
    @C.F.G that doesn't have any material on indefinite orthogonal group. – Ishan Deo Nov 08 '21 at 08:07
  • 2
    At least on the Lie algebra level, all $\mathfrak{so}(p,q)$ have complexification $\simeq \mathfrak{so}_{p+q}(\mathbb C)$. Via the correspondence of complex representations of a Lie algebra and those of its complexification, this means that a lot of their representation theory will be "isomorphic" too, confer https://math.stackexchange.com/a/3258221/96384. As discussed there, one notable exception, where each $\mathfrak{so}(p,q)$ will be a bit different, is when it comes to which representations are conjugate to which. For that, see https://math.stackexchange.com/q/3738143/96384. – Torsten Schoeneberg Nov 08 '21 at 22:02

0 Answers0