The Degree of Stiefel Manifolds

TL;DR

This paper calculates the degree of Stiefel manifolds, which are spaces of orthonormal frames, using methods from algebraic geometry, combinatorics, and invariant theory.

Contribution

It introduces a novel approach combining algebraic geometry, combinatorics, and invariant theory to compute the degree of Stiefel manifolds.

Findings

Explicit formulas for the degree of Stiefel manifolds

Application of algebraic geometry techniques to classical problems

Enhanced understanding of the geometric properties of orthonormal frame varieties

Abstract

We compute the degree of Stiefel manifolds, that is, the variety of orthonormal frames in a finite dimensional vector space. Our approach employs techniques from classical algebraic geometry, algebraic combinatorics, and classical invariant theory.