Rendiconti Lincei - Matematica e Applicazioni

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Volume 17, Issue 2, 2006, pp. 155–165

DOI: 10.4171/RLM/460

A curious identity and the volume of the root spherical simplex

Corrado De Concini (1) and Claudio Procesi (2)

(1) Dipartimento di Matematica, Università di Roma La Sapienza, Piazzale A. Moro 2, 00185, ROMA, ITALY
(2) Dipartimento di Matematica, Università di Roma La Sapienza, Piazzale A. Moro 2, 00185, ROMA, ITALY

We show a curious identity on root systems which gives the evaluation of the volume of the spherical simpleces cut by the cone generated by simple roots. In the appendix John Stembridge gives a conceptual proof of our identity.

Keywords: Root systems, Weyl groups