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Generalised spherical minors and their relations

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  • Additional Information
    • Contributors:
      Institut Camille Jordan (ICJ); École Centrale de Lyon (ECL); Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL); Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon); Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS); Algèbre, géométrie, logique (AGL); Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL); Université Claude Bernard Lyon 1 (UCBL); Université de Lyon; ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010)
    • Publication Information:
      HAL CCSD
    • Publication Date:
      2024
    • Collection:
      Université Jean Monnet – Saint-Etienne: HAL
    • Abstract:
      Let H be a spherical subgroup of minimal rank of the semisimple simply connected complex algebraic group G. We define some functions on the homogeneous space G/H that we call generalised spherical minors. When G = H x H, we recover Fomin-Zelevinsky generalised minors. We prove that generalised spherical minors satisfy some integer coefficients polynomial relations, that extend the identities of classical generalised minors due to Fomin and Zelevinsky, and that have the shape of exchange relations of LP-algebras.
    • Relation:
      info:eu-repo/semantics/altIdentifier/arxiv/2407.15114; hal-04665929; https://hal.science/hal-04665929; https://hal.science/hal-04665929/document; https://hal.science/hal-04665929/file/Generalised_spherical_minors_and_their_relations%20%282%29.pdf; ARXIV: 2407.15114
    • Online Access:
      https://hal.science/hal-04665929
      https://hal.science/hal-04665929/document
      https://hal.science/hal-04665929/file/Generalised_spherical_minors_and_their_relations%20%282%29.pdf
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • Accession Number:
      edsbas.38DF990C