Matches in SemOpenAlex for { <https://semopenalex.org/work/W1983221496> ?p ?o ?g. }
Showing items 1 to 98 of
98
with 100 items per page.
- W1983221496 endingPage "881" @default.
- W1983221496 startingPage "863" @default.
- W1983221496 abstract "We prove the B. and M. Shapiro conjecture that if the Wronskian of a set of polynomials has real roots only, then the complex span of this set of polynomials has a basis consisting of polynomials with real coefficients. This, in particular, implies the following result: If all ramification points of a parametrized rational curve φ: ℂℙ 1 → ℂℙ r lie on a circle in the Riemann sphere ℂℙ 1 , then φ maps this circle into a suitable real subspace ℝℙ r ⊂ ℂℙ r . The proof is based on the Bethe ansatz method in the Gaudin model. The key observation is that a symmetric linear operator on a Euclidean space has real spectrum. In Appendix A, we discuss properties of differential operators associated with Bethe vectors in the Gaudin model. In particular, we prove a statement, which may be useful in complex algebraic geometry; it claims that certain Schubert cycles in a Grassmannian intersect transversally if the spectrum of the corresponding Gaudin Hamiltonians is simple. In Appendix B, we formulate a conjecture on reality of orbits of critical points of master functions and prove this conjecture for master functions associated with Lie algebras of types A r , B r and C r ." @default.
- W1983221496 created "2016-06-24" @default.
- W1983221496 creator A5034010684 @default.
- W1983221496 creator A5061956834 @default.
- W1983221496 creator A5084804436 @default.
- W1983221496 date "2009-09-01" @default.
- W1983221496 modified "2023-10-02" @default.
- W1983221496 title "The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz" @default.
- W1983221496 cites W1487480094 @default.
- W1983221496 cites W1507485177 @default.
- W1983221496 cites W1553803307 @default.
- W1983221496 cites W1589445312 @default.
- W1983221496 cites W1607436585 @default.
- W1983221496 cites W1641543654 @default.
- W1983221496 cites W1675281981 @default.
- W1983221496 cites W1676075617 @default.
- W1983221496 cites W1776871335 @default.
- W1983221496 cites W2005898881 @default.
- W1983221496 cites W2012690328 @default.
- W1983221496 cites W2041852740 @default.
- W1983221496 cites W2057706156 @default.
- W1983221496 cites W2075349905 @default.
- W1983221496 cites W2078263030 @default.
- W1983221496 cites W2085476393 @default.
- W1983221496 cites W2091531266 @default.
- W1983221496 cites W2155815929 @default.
- W1983221496 cites W2953337841 @default.
- W1983221496 cites W2962876276 @default.
- W1983221496 cites W2963977949 @default.
- W1983221496 cites W2964068048 @default.
- W1983221496 cites W2964332565 @default.
- W1983221496 cites W594667561 @default.
- W1983221496 doi "https://doi.org/10.4007/annals.2009.170.863" @default.
- W1983221496 hasPublicationYear "2009" @default.
- W1983221496 type Work @default.
- W1983221496 sameAs 1983221496 @default.
- W1983221496 citedByCount "65" @default.
- W1983221496 countsByYear W19832214962012 @default.
- W1983221496 countsByYear W19832214962013 @default.
- W1983221496 countsByYear W19832214962014 @default.
- W1983221496 countsByYear W19832214962015 @default.
- W1983221496 countsByYear W19832214962016 @default.
- W1983221496 countsByYear W19832214962017 @default.
- W1983221496 countsByYear W19832214962018 @default.
- W1983221496 countsByYear W19832214962019 @default.
- W1983221496 countsByYear W19832214962020 @default.
- W1983221496 countsByYear W19832214962021 @default.
- W1983221496 countsByYear W19832214962023 @default.
- W1983221496 crossrefType "journal-article" @default.
- W1983221496 hasAuthorship W1983221496A5034010684 @default.
- W1983221496 hasAuthorship W1983221496A5061956834 @default.
- W1983221496 hasAuthorship W1983221496A5084804436 @default.
- W1983221496 hasBestOaLocation W19832214961 @default.
- W1983221496 hasConcept C114614502 @default.
- W1983221496 hasConcept C134306372 @default.
- W1983221496 hasConcept C136119220 @default.
- W1983221496 hasConcept C200741047 @default.
- W1983221496 hasConcept C202444582 @default.
- W1983221496 hasConcept C2524010 @default.
- W1983221496 hasConcept C2780990831 @default.
- W1983221496 hasConcept C33923547 @default.
- W1983221496 hasConcept C68363185 @default.
- W1983221496 hasConcept C77843276 @default.
- W1983221496 hasConcept C9376300 @default.
- W1983221496 hasConceptScore W1983221496C114614502 @default.
- W1983221496 hasConceptScore W1983221496C134306372 @default.
- W1983221496 hasConceptScore W1983221496C136119220 @default.
- W1983221496 hasConceptScore W1983221496C200741047 @default.
- W1983221496 hasConceptScore W1983221496C202444582 @default.
- W1983221496 hasConceptScore W1983221496C2524010 @default.
- W1983221496 hasConceptScore W1983221496C2780990831 @default.
- W1983221496 hasConceptScore W1983221496C33923547 @default.
- W1983221496 hasConceptScore W1983221496C68363185 @default.
- W1983221496 hasConceptScore W1983221496C77843276 @default.
- W1983221496 hasConceptScore W1983221496C9376300 @default.
- W1983221496 hasIssue "2" @default.
- W1983221496 hasLocation W19832214961 @default.
- W1983221496 hasLocation W19832214962 @default.
- W1983221496 hasLocation W19832214963 @default.
- W1983221496 hasOpenAccess W1983221496 @default.
- W1983221496 hasPrimaryLocation W19832214961 @default.
- W1983221496 hasRelatedWork W1983221496 @default.
- W1983221496 hasRelatedWork W2024069909 @default.
- W1983221496 hasRelatedWork W2036933876 @default.
- W1983221496 hasRelatedWork W2099522902 @default.
- W1983221496 hasRelatedWork W2897153210 @default.
- W1983221496 hasRelatedWork W3018072601 @default.
- W1983221496 hasRelatedWork W3026358768 @default.
- W1983221496 hasRelatedWork W4233361153 @default.
- W1983221496 hasRelatedWork W4288633133 @default.
- W1983221496 hasRelatedWork W4301136562 @default.
- W1983221496 hasVolume "170" @default.
- W1983221496 isParatext "false" @default.
- W1983221496 isRetracted "false" @default.
- W1983221496 magId "1983221496" @default.
- W1983221496 workType "article" @default.