## Schur’s $$Q$$-functions and twisted affine Lie algebras.(English)Zbl 1058.17016

Koike, Kazuhiko (ed.) et al., Combinatorial methods in representation theory. Papers of the conference on combinatorial methods in representation theory, July 21–July 31, 1998 and the conference on interaction of combinatorics and representation theory, October 26–November 6, 1998, Kyoto, Japan. Tokyo: Kinokuniya Company Ltd. (ISBN 4-314-10141-5/hbk). Adv. Stud. Pure Math. 28, 241-259 (2000).
Summary: Weight vectors of the basic representations of $$A^{(2)}_{2\ell}$$ and $$D^{(2)}_{\ell+1}$$ are studied. They are expressed in terms of Schur’s $$Q$$-functions. The up and down motion along the string of the fundamental imaginary root is described as a combinatorial game.
For the entire collection see [Zbl 0963.00024].

### MSC:

 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 05E05 Symmetric functions and generalizations 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)