Hasse-Schmidt Derivations on Grassmann Algebras: With Applications to Vertex Operators
Letterio Gatto · Parham Salehyan
Jul 2016 · IMPA Monographs Book 4 · Springer
Ebook
195
Pages
reportRatings and reviews aren’t verified Learn More
About this ebook
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 discovered at the elementary level.
About the author
Letterio Gatto received his PhD in mathematics from the University of Torino in 1993, and since then has held permanent positions at the Department of Mathematical Sciences of the Politecnico di Torino. He is currently associate professor at the Politecnico, where he offers courses on linear algebra and geometry for students in Engineering. His research interests range from Schubert calculus (classical, equivariant and quantum), algebraic curves and moduli (families of Weierstrauss points and jets of line bundles on Gorenstein curves) and integrable systems from the algebro-geometrical point of view.
Parham Salehyan graduated from Sharif University of Technology, Iran, and received his PhD in mathematics from the IMPA, Brazil, in 2003. He holds a permanent position at the Department of Mathematics of São Paulo State University - Unesp, São José do Rio Preto Campus. His research interests lie in algebraic geometry, mainly in the theory of Weierstrauss points on families of curves and, more recently, in the algebro-combinatorial aspects related to Schubert calculus.
Parham Salehyan graduated from Sharif University of Technology, Iran, and received his PhD in mathematics from the IMPA, Brazil, in 2003. He holds a permanent position at the Department of Mathematics of São Paulo State University - Unesp, São José do Rio Preto Campus. His research interests lie in algebraic geometry, mainly in the theory of Weierstrauss points on families of curves and, more recently, in the algebro-combinatorial aspects related to Schubert calculus.
Rate this ebook
Tell us what you think.
Reading information
Smartphones and tablets
Install the Google Play Books app for Android and iPad/iPhone. It syncs automatically with your account and allows you to read online or offline wherever you are.
Laptops and computers
You can listen to audiobooks purchased on Google Play using your computer's web browser.
eReaders and other devices
To read on e-ink devices like Kobo eReaders, you'll need to download a file and transfer it to your device. Follow the detailed Help Center instructions to transfer the files to supported eReaders.
