Matches in SemOpenAlex for { <https://semopenalex.org/work/W4313378568> ?p ?o ?g. }
- W4313378568 endingPage "1289" @default.
- W4313378568 startingPage "1213" @default.
- W4313378568 abstract "One can view a partial flag variety in $${mathbb {C}}^n$$ as an adjoint orbit $${mathcal {O}}_{lambda }$$ inside the Lie algebra of $$ntimes n$$ skew-Hermitian matrices. We use the orbit context to study the totally nonnegative part of a partial flag variety from an algebraic, geometric, and dynamical perspective. The paper has three main parts: (1) We introduce the totally nonnegative part of $${mathcal {O}}_{lambda }$$ , and describe it explicitly in several cases. We define a twist map on it, which generalizes (in type A) a map of Bloch, Flaschka, and Ratiu (Duke Math. J. 61(1): 41–65, 1990) on an isospectral manifold of Jacobi matrices. (2) We study gradient flows on $${mathcal {O}}_{lambda }$$ which preserve positivity, working in three natural Riemannian metrics. In the Kähler metric, positivity is preserved in many cases of interest, extending results of Galashin, Karp, and Lam (Adv. Math. 397: Paper No. 108123, 1–23, 2022; Adv. Math. 351: 614–620, 2019). In the normal metric, positivity is essentially never preserved on a generic orbit. In the induced metric, whether positivity is preserved appears to depends on the spacing of the eigenvalues defining the orbit. (3) We present two applications. First, we discuss the topology of totally nonnegative flag varieties and amplituhedra. Galashin, Karp, and Lam (2022, 2019) showed that the former are homeomorphic to closed balls, and we interpret their argument in the orbit framework. We also show that a new family of amplituhedra, which we call twisted Vandermonde amplituhedra, are homeomorphic to closed balls. Second, we discuss the symmetric Toda flow on $${mathcal {O}}_{lambda }$$ . We show that it preserves positivity, and that on the totally nonnegative part, it is a gradient flow in the Kähler metric up to applying the twist map. This extends a result of Bloch, Flaschka, and Ratiu (1990)." @default.
- W4313378568 created "2023-01-06" @default.
- W4313378568 creator A5022997192 @default.
- W4313378568 creator A5091262409 @default.
- W4313378568 date "2022-12-18" @default.
- W4313378568 modified "2023-10-16" @default.
- W4313378568 title "Gradient Flows, Adjoint Orbits, and the Topology of Totally Nonnegative Flag Varieties" @default.
- W4313378568 cites W1537957332 @default.
- W4313378568 cites W1545533256 @default.
- W4313378568 cites W1585386493 @default.
- W4313378568 cites W1593193619 @default.
- W4313378568 cites W1623071293 @default.
- W4313378568 cites W1750573494 @default.
- W4313378568 cites W1813685111 @default.
- W4313378568 cites W1908185864 @default.
- W4313378568 cites W1972362863 @default.
- W4313378568 cites W1972602556 @default.
- W4313378568 cites W1983276213 @default.
- W4313378568 cites W1986896329 @default.
- W4313378568 cites W1987225390 @default.
- W4313378568 cites W1991629562 @default.
- W4313378568 cites W1991965182 @default.
- W4313378568 cites W2002168116 @default.
- W4313378568 cites W2017943326 @default.
- W4313378568 cites W2032166319 @default.
- W4313378568 cites W2032182512 @default.
- W4313378568 cites W2034324843 @default.
- W4313378568 cites W203744636 @default.
- W4313378568 cites W2046824594 @default.
- W4313378568 cites W2054478385 @default.
- W4313378568 cites W2054663063 @default.
- W4313378568 cites W2055025634 @default.
- W4313378568 cites W2058893615 @default.
- W4313378568 cites W2060098801 @default.
- W4313378568 cites W2063934845 @default.
- W4313378568 cites W2066659058 @default.
- W4313378568 cites W2076977679 @default.
- W4313378568 cites W2087622479 @default.
- W4313378568 cites W2089996117 @default.
- W4313378568 cites W2092231151 @default.
- W4313378568 cites W2108208155 @default.
- W4313378568 cites W2127877445 @default.
- W4313378568 cites W2130714257 @default.
- W4313378568 cites W2133776435 @default.
- W4313378568 cites W2164133693 @default.
- W4313378568 cites W2171393177 @default.
- W4313378568 cites W2258126206 @default.
- W4313378568 cites W2771406229 @default.
- W4313378568 cites W2786201462 @default.
- W4313378568 cites W2786907088 @default.
- W4313378568 cites W2962980792 @default.
- W4313378568 cites W2963046719 @default.
- W4313378568 cites W2963820145 @default.
- W4313378568 cites W2963893710 @default.
- W4313378568 cites W2964071985 @default.
- W4313378568 cites W2981083573 @default.
- W4313378568 cites W3100683879 @default.
- W4313378568 cites W3100813850 @default.
- W4313378568 cites W3101013749 @default.
- W4313378568 cites W3104493577 @default.
- W4313378568 cites W3106166312 @default.
- W4313378568 cites W3111360922 @default.
- W4313378568 cites W3155723035 @default.
- W4313378568 cites W3212992884 @default.
- W4313378568 cites W4205396504 @default.
- W4313378568 cites W4205424143 @default.
- W4313378568 cites W4236579935 @default.
- W4313378568 cites W565573710 @default.
- W4313378568 cites W614920821 @default.
- W4313378568 doi "https://doi.org/10.1007/s00220-022-04540-5" @default.
- W4313378568 hasPublicationYear "2022" @default.
- W4313378568 type Work @default.
- W4313378568 citedByCount "2" @default.
- W4313378568 countsByYear W43133785682023 @default.
- W4313378568 crossrefType "journal-article" @default.
- W4313378568 hasAuthorship W4313378568A5022997192 @default.
- W4313378568 hasAuthorship W4313378568A5091262409 @default.
- W4313378568 hasBestOaLocation W43133785682 @default.
- W4313378568 hasConcept C114614502 @default.
- W4313378568 hasConcept C115491206 @default.
- W4313378568 hasConcept C127413603 @default.
- W4313378568 hasConcept C136119220 @default.
- W4313378568 hasConcept C146978453 @default.
- W4313378568 hasConcept C151730666 @default.
- W4313378568 hasConcept C165818556 @default.
- W4313378568 hasConcept C184720557 @default.
- W4313378568 hasConcept C187915474 @default.
- W4313378568 hasConcept C18903297 @default.
- W4313378568 hasConcept C196644772 @default.
- W4313378568 hasConcept C202444582 @default.
- W4313378568 hasConcept C2524010 @default.
- W4313378568 hasConcept C2776730729 @default.
- W4313378568 hasConcept C2777299769 @default.
- W4313378568 hasConcept C2779343474 @default.
- W4313378568 hasConcept C2779710842 @default.
- W4313378568 hasConcept C2780390204 @default.
- W4313378568 hasConcept C33923547 @default.
- W4313378568 hasConcept C86803240 @default.