Grassmannians of classical buildings

TL;DR

This work explores Grassmannians linked to classical buildings, including vector space Grassmannians and those of isotropic subspaces in various forms, providing a unified geometric framework.

Contribution

It introduces a comprehensive study of Grassmannians associated with classical buildings, extending classical concepts to include polar and half-spin cases.

Findings

Unified geometric framework for classical building Grassmannians

Connections between vector space Grassmannians and isotropic subspace Grassmannians

Extension of classical Grassmannian theory to polar and half-spin cases

Abstract

This book is dedicated to Grassmannians associated with buildings of classical types: usual, polar, and half-spin Grassmannians. Grassmannians of vector spaces and Grassmannians consisting of totally isotropic subspaces of non-degenerate alternating, Hermitian, and symmetric forms are special cases of these "building" Grassmannians.