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Bijection between positive clusters and projectively signed exceptional sequences
Published 10 Dec 2023 in math.RT and math.CO | (2312.05997v5)
Abstract: In 2017, Igusa and Todorov gave a bijection between signed exceptional sequences and ordered partial clusters. In this paper, we show that every term in an exceptional sequence is either relatively projective or relatively injective or both and we refine this bijection to one between projectively signed exceptional sequences and ordered partial positive clusters. We also give a characterization of relatively projective/injective objects in terms of supports of the objects in the exceptional sequence.
- Igusa, Kiyoshi. Probability distribution for exceptional sequences of type Ansubscript𝐴𝑛A_{n}italic_A start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT. arXiv:2112.04996.
- Michel, Jean. Deligne-Lusztig theoretic derivation for Weyl groups of the number of reflection factorizations of a Coxeter element. Proc of Amer Math Soc 144.3 (2016): 937–941.
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