Journal of Lie Theory

no. 1
Matsumoto theorem for skeleta
Gorelik, Maria1; Hinich, Vladimir2; Serganova, Vera3
1Weizmann Institute of Science, Rehovot, Israel
2University of Haifa, Haifa, Israel
3University of California, Berkeley, United States
Journal of Lie Theory, Special issue dedicated to the memory of Joseph A. Wolf, Volume 36 (2026) no. 1, pp. 31-41

We present a proof of a generalization of the theorem of H. Matsumoto on Coxeter groups. Our generalized version is applicable to “graphs admitting geometric realization”. The original version of the theorem for Coxeter groups is a special case when applied to the Cayley graph and the geometric representation of a Coxeter group. Our version of Matsumoto theorem is also applicable to skeleta, graphs that were defined in the recent paper [GHS24] on root Lie superalgebras.

Received:
Accepted:
Published online:
DOI: 10.5802/jolt.1417
Classification: 20F55, 51F15, 17B22, 17B67
Keywords: Coxeter groups, Weyl groups, Lie superalgebras, skeleta, Coxeter graphs

Gorelik, Maria  1 ; Hinich, Vladimir  2 ; Serganova, Vera  3

1 Weizmann Institute of Science, Rehovot, Israel
2 University of Haifa, Haifa, Israel
3 University of California, Berkeley, United States 
Gorelik, Maria; Hinich, Vladimir; Serganova, Vera. Matsumoto theorem for skeleta. Journal of Lie Theory, Special issue dedicated to the memory of Joseph A. Wolf, Volume 36 (2026) no. 1, pp. 31-41. doi: 10.5802/jolt.1417
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