Admissible Pictures and Littlewood–Richardson Crystals

Abstract

We present a one-to-one correspondence between the set of admissible pictures and the Littlewood–Richardson crystals. As a simple consequence, we shall show that the set of pictures does not depend on the choice of admissible orders.

Key Words:

• Crystals
• Littlewood–Richardson rules
• Pictures
• Young diagrams

2000 Mathematics Subject Classification:

• Primary 05E10
• Secondary 17B20, 17B37

ACKNOWLEDGMENT

First author was supported in part by JSPS Grants in Aid for Scientific Research #19540050.

Notes

Communicated by K. Misra.