Some translations in the second lowest two-sided cell of an affine Weyl group. (English) Zbl 1514.20182
Summary: We are interested in cell properties of translations in affine Weyl groups. We find out some translations in the second lowest two-sided cell of an affine Weyl group and use the translations to formulate a refinement of Jianyi Shi’s conjecture on the number of left cells in the second lowest two-sided cell. We verify the refinement for an affine Weyl group of type \(\widetilde{A}_{n-1}\) or type \(\widetilde{G}_2\).
MSC:
| 20G05 | Representation theory for linear algebraic groups |
| 20F55 | Reflection and Coxeter groups (group-theoretic aspects) |
Keywords:
affine Weyl group; extended affine Weyl groups; two-sided cell; left cell; the second lowest two-sided cell; translationsReferences:
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