Abstract
In this chapter, we describe a connection between classical invariant theory and the Grassmannian variety. Namely, for G = SL
d
(K), X the space of n × d matrices (n > d), and R = K[x
ij
∣1 ≤ i ≤ n, 1 ≤ j ≤ d] (X = Spec(R)), we have a G action on X by right multiplication, and hence a G action on R. We will show that the categorical quotient 
is isomorphic to the cone over the Grassmannian, and thus obtain a K-basis for R
G, the ring of invariants, consisting of standard monomials. In this chapter, we shall work just with the closed points of an algebraic variety.
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Lakshmibai, V., Brown, J. (2015). Relationship to Classical Invariant Theory. In: The Grassmannian Variety. Developments in Mathematics, vol 42. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3082-1_9
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DOI: https://doi.org/10.1007/978-1-4939-3082-1_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-3081-4
Online ISBN: 978-1-4939-3082-1
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