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Cell Decompositions of Quiver Flag Varieties for Nilpotent Representations of the Cyclic Quiver

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Abstract

Generalizing Schubert cells in type A and a cell decomposition of Springer fibres in type A found by L. Fresse we prove that varieties of complete flags in nilpotent representations of a cyclic quiver admit an affine cell decomposition parametrized by multi-tableaux. We show that they carry a torus operation with finitely many fixpoints. As an application of the cell decomposition we obtain a vector space basis of certain modules (for quiver Hecke algebras of nilpotent representations of this quiver), similar modules have been studied by Kato as analogues of standard modules.

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Acknowledgements

I would like to thank Peter Mc Namara for pointing out that the multiplicity spaces can be zero and therefore, Kato’s work can not directly be applied. Also I would like to thank the anonymous referee for a detailed reading. Furthermore, I would like to mention financial support from the CRC 701 in Bielefeld and the SPP 1388 (Schwerpunktprogramm Darstellungstheorie) by covering travel costs and research stays.

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  1. Faculty of Mathematics, Bielefeld University, Postfach 100 131, D-33501, Bielefeld, Germany

    Julia Sauter

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  1. Julia Sauter
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Presented by Peter Littelmann.

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Sauter, J. Cell Decompositions of Quiver Flag Varieties for Nilpotent Representations of the Cyclic Quiver. Algebr Represent Theor 20, 1323–1340 (2017). https://doi.org/10.1007/s10468-017-9689-9

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