Multiplicative formulas in Schubert calculus and quiver representation
نویسندگان
چکیده
منابع مشابه
The Connection between Representation Theory and Schubert Calculus
The structure constants cλμ determine the classical Schubert calculus on G(m,n). It has been known for some time that the integers cλμ in formulas (1) and (2) coincide. Following the work of Giambelli [G1] [G2], this is proved formally by relating both products to the multiplication of Schur S-polynomials; a precise argument along these lines was given by Lesieur [Les]. It is natural to ask for...
متن کاملMultiplicative formulas in Cohomology of G/P and in quiver representations
Consider a partial flag variety X which is not a grassmaninan. Consider also its cohomology ring H∗(X,Z) endowed with the base formed by the Poincaré dual classes of the Schubert varieties. In [Ricar], E. Richmond showed that some coefficient structure of the product in H∗(X,Z) are products of two such coefficients for smaller flag varieties. Consider now a quiver without oriented cycle. If α a...
متن کاملSchubert Calculus and Puzzles
1. Interval positroid varieties 1 1.1. Schubert varieties 1 1.2. Schubert calculus 2 1.3. First positivity result 3 1.4. Interval rank varieties 5 2. Vakil’s Littlewood-Richardson rule 7 2.1. Combinatorial shifting 7 2.2. Geometric shifting 7 2.3. Vakil’s degeneration order 9 2.4. Partial puzzles 10 3. Equivariant and Kextensions 11 3.1. K-homology 11 3.2. K-cohomology 12 3.3. Equivariant K-the...
متن کاملEigenvalues and Schubert Calculus
We describe recent work of Klyachko, Totaro, Knutson, and Tao, that characterizes eigenvalues of sums of Hermitian matrices, and decomposition of tensor products of representations of GLn(C). We explain related applications to invariant factors of products of matrices, intersections in Grassmann varieties, and singular values of sums and products of arbitrary matrices.
متن کاملContemporary Schubert Calculus and Schubert Geometry
Schubert calculus refers to the calculus of enumerative geometry, which is the art of counting geometric figures determined by given incidence conditions. For example, how many lines in projective 3-space meet four given lines? This was developed in the 19th century and presented in the classic treatise ”Kälkul der abzählanden Geometrie” by Herman Cäser Hannibal Schubert in 1879. Schubert, Pier...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2011
ISSN: 0019-3577
DOI: 10.1016/j.indag.2011.08.004