Conformal embedding and twisted theta functions at level one

Abstract

In this paper, we consider the conformal embedding of s o ( r ) \mathfrak {so}(r) into s l ( r ) \mathfrak {sl}(r) and study relations between level one SO ⁡ ( r ) \operatorname {SO}(r) -theta functions and twisted SL ⁡ ( r ) \operatorname {SL}(r) -theta functions coming from parahoric moduli spaces. In particular, we give another proof of a theorem by Pauly-Ramanan [J. London Math. Soc. (2) 63 (2001), pp. 513–532].