Matches in SemOpenAlex for { <https://semopenalex.org/work/W4308393426> ?p ?o ?g. }
Showing items 1 to 67 of
67
with 100 items per page.
- W4308393426 abstract "Berenstein and Kazhdan's theory of geometric crystals gives rise to two commuting families of geometric crystal operators acting on the space of complex $m times n$ matrices. These are birational actions, which we view as a crystal-theoretic analogue of the usual action of ${rm SL}_m times {rm SL}_n$ on $m times n$ matrices. We prove that the field of rational invariants (and ring of polynomial invariants) of each family of geometric crystal operators is generated by a set of algebraically independent polynomials, which are generalizations of the elementary symmetric polynomials in $m$ (or $n$) variables. We also give a set of algebraically independent generators for the intersection of these fields, and we explain how these fields are situated inside the larger fields of geometric $R$-matrix invariants, which were studied by Lam and the third-named author under the name loop symmetric functions. The key tool in our proof is the geometric RSK correspondence of Noumi and Yamada, which we show to be an isomorphism of geometric crystals. In an appendix jointly written with Thomas Lam, we prove the fundamental theorem of loop symmetric functions, which says that the polynomial invariants of the geometric $R$-matrix are generated by the loop elementary symmetric functions." @default.
- W4308393426 created "2022-11-11" @default.
- W4308393426 creator A5003538686 @default.
- W4308393426 creator A5039956279 @default.
- W4308393426 creator A5040028648 @default.
- W4308393426 creator A5087568902 @default.
- W4308393426 date "2021-12-01" @default.
- W4308393426 modified "2023-10-14" @default.
- W4308393426 title "Crystal invariant theory I: Geometric RSK" @default.
- W4308393426 doi "https://doi.org/10.48550/arxiv.2112.00524" @default.
- W4308393426 hasPublicationYear "2021" @default.
- W4308393426 type Work @default.
- W4308393426 citedByCount "0" @default.
- W4308393426 crossrefType "posted-content" @default.
- W4308393426 hasAuthorship W4308393426A5003538686 @default.
- W4308393426 hasAuthorship W4308393426A5039956279 @default.
- W4308393426 hasAuthorship W4308393426A5040028648 @default.
- W4308393426 hasAuthorship W4308393426A5087568902 @default.
- W4308393426 hasBestOaLocation W43083934261 @default.
- W4308393426 hasConcept C114614502 @default.
- W4308393426 hasConcept C115624301 @default.
- W4308393426 hasConcept C118615104 @default.
- W4308393426 hasConcept C134306372 @default.
- W4308393426 hasConcept C136119220 @default.
- W4308393426 hasConcept C185592680 @default.
- W4308393426 hasConcept C190470478 @default.
- W4308393426 hasConcept C202444582 @default.
- W4308393426 hasConcept C203436722 @default.
- W4308393426 hasConcept C203701370 @default.
- W4308393426 hasConcept C33923547 @default.
- W4308393426 hasConcept C37914503 @default.
- W4308393426 hasConcept C63036529 @default.
- W4308393426 hasConcept C8010536 @default.
- W4308393426 hasConcept C90119067 @default.
- W4308393426 hasConcept C9485509 @default.
- W4308393426 hasConceptScore W4308393426C114614502 @default.
- W4308393426 hasConceptScore W4308393426C115624301 @default.
- W4308393426 hasConceptScore W4308393426C118615104 @default.
- W4308393426 hasConceptScore W4308393426C134306372 @default.
- W4308393426 hasConceptScore W4308393426C136119220 @default.
- W4308393426 hasConceptScore W4308393426C185592680 @default.
- W4308393426 hasConceptScore W4308393426C190470478 @default.
- W4308393426 hasConceptScore W4308393426C202444582 @default.
- W4308393426 hasConceptScore W4308393426C203436722 @default.
- W4308393426 hasConceptScore W4308393426C203701370 @default.
- W4308393426 hasConceptScore W4308393426C33923547 @default.
- W4308393426 hasConceptScore W4308393426C37914503 @default.
- W4308393426 hasConceptScore W4308393426C63036529 @default.
- W4308393426 hasConceptScore W4308393426C8010536 @default.
- W4308393426 hasConceptScore W4308393426C90119067 @default.
- W4308393426 hasConceptScore W4308393426C9485509 @default.
- W4308393426 hasLocation W43083934261 @default.
- W4308393426 hasOpenAccess W4308393426 @default.
- W4308393426 hasPrimaryLocation W43083934261 @default.
- W4308393426 hasRelatedWork W1927071250 @default.
- W4308393426 hasRelatedWork W1996580892 @default.
- W4308393426 hasRelatedWork W2009896212 @default.
- W4308393426 hasRelatedWork W2153887426 @default.
- W4308393426 hasRelatedWork W2439115288 @default.
- W4308393426 hasRelatedWork W3102075949 @default.
- W4308393426 hasRelatedWork W3109111491 @default.
- W4308393426 hasRelatedWork W3126773016 @default.
- W4308393426 hasRelatedWork W3179755564 @default.
- W4308393426 hasRelatedWork W4302393486 @default.
- W4308393426 isParatext "false" @default.
- W4308393426 isRetracted "false" @default.
- W4308393426 workType "article" @default.