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Schubert functors and Schubert polynomials by Witold Kraśkiewicz; Piotr Pragacz is a Mathematics article available to read on EtoBox.
What is Schubert functors and Schubert polynomials about?
We construct a family of functors assigning an R-module to a flag of R-modules, where R is a commutative ring. As particular instances, we get flagged Schur functors and Schubert functors, the latter family being indexed by permutations. We identify Schubert functors for vexillary permutations with some flagged Schur functors, thus establishing a functorial analogue of a theorem of Lascoux and Schützenberger from C. R. Acad. Sci. Paris Sér. I Math. 294 (1982) 447 and of Wachs from J. Combin. Theory Ser. A 40 (1985) 276. Over an infinite field, we study the trace of a Schubert module, which is a cyclic module over a Borel subgroup B, restricted to the maximal torus. The main result of the paper says that this trace is equal to the corresponding Schubert polynomial of Lascoux and Schützenberger (C.
Who reads Schubert functors and Schubert polynomials?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Witold Kraśkiewicz; Piotr Pragacz
- Publisher
- Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0195-6698)
- Published
- 2004
- Language
- EN
- Field
- Mathematics (Physical Sciences)