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I am interested in the principal series (unitary irreducible) representations of $Spin(n-1,1)$, and in the generalized Pancherel's formula for the delta function on the group in terms of a sum (and an integral) of characters:

$$ \delta(g) = \int \dots \sum_{\dots} \text{tr} W_{\dots} (g), $$

where $\dots$ represent the continuous and discrete parameters labeling the irrep from the principal series.

I already know that principal irreps have been classified for $Spin(2,1) \sim SL(2,\mathbb{R})$ and $Spin(3,1)\sim SL(2,\mathbb{C})$. I am interested in the general case of $Spin(n-1, 1)$, or at least in $Spin(5,1)$ and $Spin(7,1)$.

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    $\begingroup$ did you try google search? $\endgroup$
    – Venkataramana
    Commented Jul 17, 2017 at 4:17
  • $\begingroup$ @Venkataramana I don't see the point of your comment. Yes, I searched for this, and I haven't find anything useful. Did you find something useful? If I missed it, please share your findings with me. $\endgroup$
    – Prof. Legolasov
    Commented Jul 17, 2017 at 4:40
  • $\begingroup$ See Unitary Representations of O(p,q) $\endgroup$
    – Jeffrey Adams
    Commented Jul 20, 2017 at 3:42

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Knapp (1986, p. 736) attributes the Plancherel formula for real-rank-one groups to Okamoto (1965), Hirai (1966), and Harish-Chandra (1966). More details in Sally-Warner (1973), Miatello (1979).

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