no. 3
Lie superalgebras generated by reflections in Weyl groups of classical type
Drupieski, Christopher Martin1 orcid; Kujawa, Jonathan Robert2 orcid 
1Department of Mathematical Sciences, DePaul University, Chicago, IL 60614, USA
2Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA
Annals of Representation Theory, Volume 3 (2026) no. 3, pp. 399-438

We consider the finite Weyl groups of classical type ($W(A_r)$ for $r \ge 1$, $W(B_r) = W(C_r)$ for $r \ge 2$, and $W(D_r)$ for $r \ge 4$) as supergroups in which the reflections are of odd superdegree. Viewing the corresponding complex group algebras as Lie superalgebras via the graded commutator bracket, we determine the structure of the Lie sub-superalgebras generated by the sets of reflections. In each case, this Lie superalgebra is equal to the full derived subalgebra of the group algebra plus the span of the class sums of the reflections.

Received:
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Accepted:
Published online:
DOI: 10.5802/art.45
Classification: 17B10, 20B30
Keywords: Lie superalgebras, supergroups, type B Weyl groups, type D Weyl groups

Drupieski, Christopher Martin  1 ; Kujawa, Jonathan Robert  2

1 Department of Mathematical Sciences, DePaul University, Chicago, IL 60614, USA
2 Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Drupieski, Christopher Martin; Kujawa, Jonathan Robert. Lie superalgebras generated by reflections in Weyl groups of classical type. Annals of Representation Theory, Volume 3 (2026) no. 3, pp. 399-438. doi: 10.5802/art.45
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