Polynomials and the mod 2 Steenrod Algebra

Polynomials and the mod 2 Steenrod Algebra by Grant Walker, published by Cambridge University Press in 2018, is a comprehensive exploration of the connections between the mod 2 Steenrod algebra and modular representations of matrix groups over the field F of two elements. This edition spans 355 pages and is presented in English, offering a detailed examination of Peterson’s ‘hit problem’ related to the action of the Steenrod algebra on polynomials, which remains an open question in many cases.

Readers will find an in-depth analysis of various mathematical concepts, including decompositions of integers and the structure of Hopf algebras, as well as the Steinberg representation of GL(n,F). The book serves as a graduate-level textbook, focusing on the algebraic aspects of the Steenrod algebra while also paving the way for further discussions in modular representations. This first volume lays the groundwork for understanding the intricate relationships within algebraic topology and discrete mathematics.