2022/11/13 by Yasmine Fittouhi, Anthony D. Joseph, Fittouhi, Yasmine +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Partial Differential Equations #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2211.06851
openalex publication_date 2022/11/13 · openalex created_date 2022/11/23 · openalex updated_date 2026/07/28
A "Composition map" is constructed, leaning heavily on earlier work [Y. Fittouhi and A. Joseph, Parabolic adjoint action, Weierstrass sections and components of the nilfibre in type A, Indag Math. and Y. Fittouhi and A. Joseph, The canonical component of the nilfibre for parabolic adjoint action, Weierstrass sections in type A, preprint, Weizmann, 2021]. It defines a composition tableau which recovers the "canonical" Weierstrass section e+V described in the first paper above. Moreover without reference to this earlier work, it is then shown that e+V is indeed a Weierstrass section. This results in a huge simplification. Moreover one may read off from the composition tableau the "VS quadruplets'' of the second of the above papers, thereby describing the "canonical component" of the nil-fibre in which e lies but does not of itself determine.