Grassmannian (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Grassmannian" in English language version.

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ams.org

mathscinet.ams.org

Griffiths, Phillip; Harris, Joseph (1994), Principles of algebraic geometry, Wiley Classics Library (2nd ed.), New York: John Wiley & Sons, p. 211, ISBN 0-471-05059-8, MR 1288523, Zbl 0836.14001
Cartan, Élie (1981) [1938]. The theory of spinors. New York: Dover Publications. ISBN 978-0-486-64070-9. MR 0631850.
Morel, Fabien; Voevodsky, Vladimir (1999). "A¹-homotopy theory of schemes" (PDF). Publications Mathématiques de l'IHÉS. 90 (90): 45–143. doi:10.1007/BF02698831. ISSN 1618-1913. MR 1813224. S2CID 14420180. Retrieved 2008-09-05., see section 4.3., pp. 137–140

arxiv.org

Witten, Edward (1993). "The Verlinde algebra and the cohomology of the Grassmannian". arXiv:hep-th/9312104.
Mukhin, E.; Tarasov, V.; Varchenko, A. (2009). "Schubert Calculus and representations of the general linear group". J. Amer. Math. Soc. 22 (4). American Mathematical Society: 909–940. arXiv:0711.4079. Bibcode:2009JAMS...22..909M. doi:10.1090/S0894-0347-09-00640-7.
Chakravarty, S.; Kodama, Y. (July 2009). "Soliton Solutions of the KP Equation and Application to Shallow Water Waves". Studies in Applied Mathematics. 123: 83–151. arXiv:0902.4433. doi:10.1111/j.1467-9590.2009.00448.x. S2CID 18390193.
Kodama, Yuji; Williams, Lauren (December 2014). "KP solitons and total positivity for the Grassmannian". Inventiones Mathematicae. 198 (3): 637–699. arXiv:1106.0023. Bibcode:2014InMat.198..637K. doi:10.1007/s00222-014-0506-3. S2CID 51759294.
Arkani-Hamed, Nima; Trnka, Jaroslav (2013). "The Amplituhedron". Journal of High Energy Physics. 2014 (10): 30. arXiv:1312.2007. Bibcode:2014JHEP...10..030A. doi:10.1007/JHEP10(2014)030. S2CID 7717260.

asu.edu

public.asu.edu

Pavan Turaga, Ashok Veeraraghavan, Rama Chellappa: Statistical analysis on Stiefel and Grassmann manifolds with applications in computer vision, CVPR 23–28 June 2008, IEEE Conference on Computer Vision and Pattern Recognition, 2008, ISBN 978-1-4244-2242-5, pp. 1–8 (abstract, full text)

books.google.com

Cartan, Élie (1981) [1938]. The theory of spinors. New York: Dover Publications. ISBN 978-0-486-64070-9. MR 0631850.

doi.org

Shafarevich 2013, p. 42, Example 1.24. Shafarevich, Igor R. (2013). Basic Algebraic Geometry 1. Springer Science. doi:10.1007/978-3-642-37956-7. ISBN 978-0-387-97716-4.
Harnad, J.; Shnider, S. (1992). "Isotropic geometry and twistors in higher dimensions. I. The generalized Klein correspondence and spinor flags in even dimensions". Journal of Mathematical Physics. 33 (9). American Institute of Physics: 3197–3208. Bibcode:1992JMP....33.3197H. doi:10.1063/1.529538.
Harnad, J.; Shnider, S. (1995). "Isotropic geometry and twistors in higher dimensions. II. Odd dimensions, reality conditions, and twistor superspaces". Journal of Mathematical Physics. 36 (9). American Institute of Physics: 1945–1970. Bibcode:1995JMP....36.1945H. doi:10.1063/1.531096.
Narasimhan, M. S.; Ramanan, S. (1961). "Existence of Universal Connections". American Journal of Mathematics. 83 (3): 563–572. doi:10.2307/2372896. hdl:10338.dmlcz/700905. JSTOR 2372896. S2CID 123324468.
Narasimhan, M. S.; Ramanan, S. (1963). "Existence of Universal Connections II". American Journal of Mathematics. 85 (2): 223–231. doi:10.2307/2373211. JSTOR 2373211.
Mukhin, E.; Tarasov, V.; Varchenko, A. (2009). "Schubert Calculus and representations of the general linear group". J. Amer. Math. Soc. 22 (4). American Mathematical Society: 909–940. arXiv:0711.4079. Bibcode:2009JAMS...22..909M. doi:10.1090/S0894-0347-09-00640-7.
Date, Etsuro; Jimbo, Michio; Kashiwara, Masaki; Miwa, Tetsuji (1981). "Operator Approach to the Kadomtsev-Petviashvili Equation–Transformation Groups for Soliton Equations III–". Journal of the Physical Society of Japan. 50 (11). Physical Society of Japan: 3806–3812. Bibcode:1981JPSJ...50.3806D. doi:10.1143/jpsj.50.3806. ISSN 0031-9015.
Jimbo, Michio; Miwa, Tetsuji (1983). "Solitons and infinite-dimensional Lie algebras". Publications of the Research Institute for Mathematical Sciences. 19 (3). European Mathematical Society Publishing House: 943–1001. doi:10.2977/prims/1195182017. ISSN 0034-5318.
Harnad, J.; Balogh, F. (2021). Tau functions and Their Applications, Chapts. 4 and 5. Cambridge Monographs on Mathematical Physics. Cambridge, U.K.: Cambridge University Press. doi:10.1017/9781108610902. ISBN 9781108610902. S2CID 222379146.
Harnad, J.; Balogh, F. (2021). Tau functions and Their Applications, Chapt. 7. Cambridge Monographs on Mathematical Physics. Cambridge, U.K.: Cambridge University Press. doi:10.1017/9781108610902. ISBN 9781108610902. S2CID 222379146.
Chakravarty, S.; Kodama, Y. (July 2009). "Soliton Solutions of the KP Equation and Application to Shallow Water Waves". Studies in Applied Mathematics. 123: 83–151. arXiv:0902.4433. doi:10.1111/j.1467-9590.2009.00448.x. S2CID 18390193.
Kodama, Yuji; Williams, Lauren (December 2014). "KP solitons and total positivity for the Grassmannian". Inventiones Mathematicae. 198 (3): 637–699. arXiv:1106.0023. Bibcode:2014InMat.198..637K. doi:10.1007/s00222-014-0506-3. S2CID 51759294.
Arkani-Hamed, Nima; Trnka, Jaroslav (2013). "The Amplituhedron". Journal of High Energy Physics. 2014 (10): 30. arXiv:1312.2007. Bibcode:2014JHEP...10..030A. doi:10.1007/JHEP10(2014)030. S2CID 7717260.
Morel, Fabien; Voevodsky, Vladimir (1999). "A¹-homotopy theory of schemes" (PDF). Publications Mathématiques de l'IHÉS. 90 (90): 45–143. doi:10.1007/BF02698831. ISSN 1618-1913. MR 1813224. S2CID 14420180. Retrieved 2008-09-05., see section 4.3., pp. 137–140

handle.net

hdl.handle.net

Narasimhan, M. S.; Ramanan, S. (1961). "Existence of Universal Connections". American Journal of Mathematics. 83 (3): 563–572. doi:10.2307/2372896. hdl:10338.dmlcz/700905. JSTOR 2372896. S2CID 123324468.
Sato, Mikio (October 1981). "Soliton Equations as Dynamical Systems on Infinite Dimensional Grassmann Manifolds (Random Systems and Dynamical Systems)". 数理解析研究所講究録. 439: 30–46. hdl:2433/102800.

harvard.edu

ui.adsabs.harvard.edu

Harnad, J.; Shnider, S. (1992). "Isotropic geometry and twistors in higher dimensions. I. The generalized Klein correspondence and spinor flags in even dimensions". Journal of Mathematical Physics. 33 (9). American Institute of Physics: 3197–3208. Bibcode:1992JMP....33.3197H. doi:10.1063/1.529538.
Harnad, J.; Shnider, S. (1995). "Isotropic geometry and twistors in higher dimensions. II. Odd dimensions, reality conditions, and twistor superspaces". Journal of Mathematical Physics. 36 (9). American Institute of Physics: 1945–1970. Bibcode:1995JMP....36.1945H. doi:10.1063/1.531096.
Mukhin, E.; Tarasov, V.; Varchenko, A. (2009). "Schubert Calculus and representations of the general linear group". J. Amer. Math. Soc. 22 (4). American Mathematical Society: 909–940. arXiv:0711.4079. Bibcode:2009JAMS...22..909M. doi:10.1090/S0894-0347-09-00640-7.
Date, Etsuro; Jimbo, Michio; Kashiwara, Masaki; Miwa, Tetsuji (1981). "Operator Approach to the Kadomtsev-Petviashvili Equation–Transformation Groups for Soliton Equations III–". Journal of the Physical Society of Japan. 50 (11). Physical Society of Japan: 3806–3812. Bibcode:1981JPSJ...50.3806D. doi:10.1143/jpsj.50.3806. ISSN 0031-9015.
Kodama, Yuji; Williams, Lauren (December 2014). "KP solitons and total positivity for the Grassmannian". Inventiones Mathematicae. 198 (3): 637–699. arXiv:1106.0023. Bibcode:2014InMat.198..637K. doi:10.1007/s00222-014-0506-3. S2CID 51759294.
Arkani-Hamed, Nima; Trnka, Jaroslav (2013). "The Amplituhedron". Journal of High Energy Physics. 2014 (10): 30. arXiv:1312.2007. Bibcode:2014JHEP...10..030A. doi:10.1007/JHEP10(2014)030. S2CID 7717260.

ieee.org

ieeexplore.ieee.org

Pavan Turaga, Ashok Veeraraghavan, Rama Chellappa: Statistical analysis on Stiefel and Grassmann manifolds with applications in computer vision, CVPR 23–28 June 2008, IEEE Conference on Computer Vision and Pattern Recognition, 2008, ISBN 978-1-4244-2242-5, pp. 1–8 (abstract, full text)

jstor.org

Narasimhan, M. S.; Ramanan, S. (1961). "Existence of Universal Connections". American Journal of Mathematics. 83 (3): 563–572. doi:10.2307/2372896. hdl:10338.dmlcz/700905. JSTOR 2372896. S2CID 123324468.
Narasimhan, M. S.; Ramanan, S. (1963). "Existence of Universal Connections II". American Journal of Mathematics. 85 (2): 223–231. doi:10.2307/2373211. JSTOR 2373211.

numdam.org

archive.numdam.org

Morel, Fabien; Voevodsky, Vladimir (1999). "A¹-homotopy theory of schemes" (PDF). Publications Mathématiques de l'IHÉS. 90 (90): 45–143. doi:10.1007/BF02698831. ISSN 1618-1913. MR 1813224. S2CID 14420180. Retrieved 2008-09-05., see section 4.3., pp. 137–140

quantamagazine.org

Hartnett, Kevin (16 December 2020). "A Mathematician's Unanticipated Journey Through the Physical World". Quanta Magazine. Retrieved 17 December 2020.

semanticscholar.org

api.semanticscholar.org

Narasimhan, M. S.; Ramanan, S. (1961). "Existence of Universal Connections". American Journal of Mathematics. 83 (3): 563–572. doi:10.2307/2372896. hdl:10338.dmlcz/700905. JSTOR 2372896. S2CID 123324468.
Harnad, J.; Balogh, F. (2021). Tau functions and Their Applications, Chapts. 4 and 5. Cambridge Monographs on Mathematical Physics. Cambridge, U.K.: Cambridge University Press. doi:10.1017/9781108610902. ISBN 9781108610902. S2CID 222379146.
Harnad, J.; Balogh, F. (2021). Tau functions and Their Applications, Chapt. 7. Cambridge Monographs on Mathematical Physics. Cambridge, U.K.: Cambridge University Press. doi:10.1017/9781108610902. ISBN 9781108610902. S2CID 222379146.
Chakravarty, S.; Kodama, Y. (July 2009). "Soliton Solutions of the KP Equation and Application to Shallow Water Waves". Studies in Applied Mathematics. 123: 83–151. arXiv:0902.4433. doi:10.1111/j.1467-9590.2009.00448.x. S2CID 18390193.
Kodama, Yuji; Williams, Lauren (December 2014). "KP solitons and total positivity for the Grassmannian". Inventiones Mathematicae. 198 (3): 637–699. arXiv:1106.0023. Bibcode:2014InMat.198..637K. doi:10.1007/s00222-014-0506-3. S2CID 51759294.
Arkani-Hamed, Nima; Trnka, Jaroslav (2013). "The Amplituhedron". Journal of High Energy Physics. 2014 (10): 30. arXiv:1312.2007. Bibcode:2014JHEP...10..030A. doi:10.1007/JHEP10(2014)030. S2CID 7717260.
Morel, Fabien; Voevodsky, Vladimir (1999). "A¹-homotopy theory of schemes" (PDF). Publications Mathématiques de l'IHÉS. 90 (90): 45–143. doi:10.1007/BF02698831. ISSN 1618-1913. MR 1813224. S2CID 14420180. Retrieved 2008-09-05., see section 4.3., pp. 137–140

springer.com

link.springer.com

Shafarevich 2013, p. 42, Example 1.24. Shafarevich, Igor R. (2013). Basic Algebraic Geometry 1. Springer Science. doi:10.1007/978-3-642-37956-7. ISBN 978-0-387-97716-4.

worldcat.org

search.worldcat.org

Lee 2012, p. 22, Example 1.36. Lee, John M. (2012). Introduction to Smooth Manifolds. Graduate Texts in Mathematics. Vol. 218 (Second ed.). New York London: Springer-Verlag. ISBN 978-1-4419-9981-8. OCLC 808682771.
Date, Etsuro; Jimbo, Michio; Kashiwara, Masaki; Miwa, Tetsuji (1981). "Operator Approach to the Kadomtsev-Petviashvili Equation–Transformation Groups for Soliton Equations III–". Journal of the Physical Society of Japan. 50 (11). Physical Society of Japan: 3806–3812. Bibcode:1981JPSJ...50.3806D. doi:10.1143/jpsj.50.3806. ISSN 0031-9015.
Jimbo, Michio; Miwa, Tetsuji (1983). "Solitons and infinite-dimensional Lie algebras". Publications of the Research Institute for Mathematical Sciences. 19 (3). European Mathematical Society Publishing House: 943–1001. doi:10.2977/prims/1195182017. ISSN 0034-5318.
Morel, Fabien; Voevodsky, Vladimir (1999). "A¹-homotopy theory of schemes" (PDF). Publications Mathématiques de l'IHÉS. 90 (90): 45–143. doi:10.1007/BF02698831. ISSN 1618-1913. MR 1813224. S2CID 14420180. Retrieved 2008-09-05., see section 4.3., pp. 137–140

zbmath.org

Griffiths, Phillip; Harris, Joseph (1994), Principles of algebraic geometry, Wiley Classics Library (2nd ed.), New York: John Wiley & Sons, p. 211, ISBN 0-471-05059-8, MR 1288523, Zbl 0836.14001