| 书目名称 | Hasse-Schmidt Derivations on Grassmann Algebras |
| 副标题 | With Applications to |
| 编辑 | Letterio Gatto,Parham Salehyan |
| 视频video | |
| 概述 | Offers a comprehensive approach to advanced topics such as linear ODEs and generalized Wronskians, Schubert calculus for ordinary Grassmannians and vertex operators arising from the representation the |
| 丛书名称 | IMPA Monographs |
| 图书封面 |  |
| 描述 | This book provides a comprehensive advanced multi-linear algebra course based on the concept of Hasse-Schmidt derivations on a Grassmann algebra (an analogue of the Taylor expansion for real-valued functions), and shows how this notion provides a natural framework for many ostensibly unrelated subjects: traces of an endomorphism and the Cayley-Hamilton theorem, generic linear ODEs and their Wronskians, the exponential of a matrix with indeterminate entries (Putzer‘s method revisited), universal decomposition of a polynomial in the product of two monic polynomials of fixed smaller degree, Schubert calculus for Grassmannian varieties, and vertex operators obtained with the help of Schubert calculus tools (Giambelli‘s formula). Significant emphasis is placed on the characterization of decomposable tensors of an exterior power of a free abelian group of possibly infinite rank, which then leads to the celebrated Hirota bilinear form of the Kadomtsev-Petviashvili (KP) hierarchy describing the Plücker embedding of an infinite-dimensional Grassmannian. By gathering ostensibly disparate issues together under a unified perspective, the book reveals how even the most advanced topics can be di |
| 出版日期 | Book 2016 |
| 关键词 | Grassmann algebras; Schubert calculus; Vertex operators; Symmetric functions; KP hierarchy; Hasse-Schmidt |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-319-31842-4 |
| isbn_softcover | 978-3-319-81134-5 |
| isbn_ebook | 978-3-319-31842-4 |
| copyright | Springer International Publishing Switzerland 2016 |
发表于 2025-3-21 20:00:26
