Puzzles in K-homology of Grassmannians
نویسنده
چکیده
Knutson, Tao, and Woodward [KTW04] formulated a Littlewood–Richardson rule for the cohomology ring of Grassmannians in terms of puzzles. Vakil [Vak06] and Wheeler–Zinn-Justin [WZ16] have found additional triangular puzzle pieces that allow one to express structure constants for K-theory of Grassmannians. Here we introduce two other puzzle pieces of hexagonal shape, each of which gives a Littlewood–Richardson rule for K-homology of Grassmannians. We also explore the corresponding eight versions of K-theoretic Littlewood–Richardson tableaux.
منابع مشابه
Homology rigidity of Grassmannians
Combining the theory of Gröbner basis with the Schubert presentation for the cohomology of Grassmannians [DZ1], we generalize the homology rigidity results known for the classical Grassmanians to the exceptional cases. Email: [email protected] 2000 Mathematics subject classification: 55S37
متن کاملHomology rigidity of Grassmannians Dedicated to Professor Wenjun Wu on his 90th birthday
Applying the theory of Gröbner basis to the Schubert presentation for the cohomology of Grassmannians [DZ1], we extend the homology rigidity results known for the classical Grassmanians to the exceptional cases. 2000 Mathematics subject classification: 55S37
متن کاملSome Extensions of the Notion of Loop Grassmannians
We report an ongoing attempt to establish in algebraic geometry certain analogues of topological ideas, The main goal is to associate to a scheme X over a commutative ring k its “relative motivic homology” which is again an algebro geometric object over the base k. This is motivated by Number Theory, so the Poincare duality for this relative motivic homology should be an algebro geometric incar...
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 کاملMutations of Puzzles and Equivariant Cohomology of Two-step Flag Varieties
We introduce a mutation algorithm for puzzles that is a threedirection analogue of the classical jeu de taquin algorithm for semistandard tableaux. We apply this algorithm to prove our conjectured puzzle formula for the equivariant Schubert structure constants of two-step flag varieties. This formula gives an expression for the structure constants that is positive in the sense of Graham. Thanks...
متن کامل