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abstract: 'The relation of crystal bases with $q$-identities is discussed, and some new results on crystals and $q$-identities associated with the affine Lie algebra $C_n^{(1)}$ are presented.'
address:
- 'Department of Informatics and Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan'
- 'Department of Mathematics 2-279, M.I.T., Cambridge, MA 02139, U.S.A. andDepartment of Mathematics, University of California, One Shields Avenue, Davis, CA 95616-8633, U.S.A.'
- 'Department of Mathematics, 460 McBryde Hall, Virginia Tech, Blacksburg, VA 24061-0123, U.S.A'
author:
- Masato Okado
- Anne Schilling
- Mark Shimozono
title: 'Crystal bases and $q$-identities'
---

Introduction
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The purpose of this paper is two-fold. First, we would like to advocate the importance of crystal theory to the theory of $q$-series. In particular crystal base theory provides a unifying and general setting for a large class of $q$-identities. Second, as evidence, some new identities associated to the affine Lie algebra $C_n^{(1)}$ are presented. The emphasis here will not be on the completeness of the results since the field is evolving quite rapidly, but rather on the presentation of the main ideas and techniques used.

The Rogers–Ramanujan identities are undoubtably the most famous $q$-series identities. They are given 