# KClass ^ ZZ -- computes powers of an equivariant K-classes

## Synopsis

• Operator: ^
• Usage:
C^n
• Inputs:
• Outputs:
• , the n-th power of C

## Description

This method computes the $n$-th power of an equivariant $K$-class $C$.

 i1 : Gr24 = generalizedFlagVariety("A",3,{2}); --the Grassmannian of projective lines in projective 3-space i2 : O1 = ampleKClass Gr24 -- the O(1) bundle on Gr24 as an equivariant K-class o2 = an equivariant K-class on a GKM variety o2 : KClass i3 : O2 = O1^2 o3 = an equivariant K-class on a GKM variety o3 : KClass i4 : peek O2 o4 = KClass{variety => a GKM variety with an action of a 4-dimensional torus} 2 2 KPolynomials => HashTable{{set {0, 1}} => T T } 0 1 2 2 {set {0, 2}} => T T 0 2 2 2 {set {0, 3}} => T T 0 3 2 2 {set {1, 2}} => T T 1 2 2 2 {set {1, 3}} => T T 1 3 2 2 {set {2, 3}} => T T 2 3 i5 : Oneg1 = O1^(-1) o5 = an equivariant K-class on a GKM variety o5 : KClass i6 : peek Oneg1 o6 = KClass{variety => a GKM variety with an action of a 4-dimensional torus} -1 -1 KPolynomials => HashTable{{set {0, 1}} => T T } 0 1 -1 -1 {set {0, 2}} => T T 0 2 -1 -1 {set {0, 3}} => T T 0 3 -1 -1 {set {1, 2}} => T T 1 2 -1 -1 {set {1, 3}} => T T 1 3 -1 -1 {set {2, 3}} => T T 2 3

## Caveat

$n$ is allowed to be negative only when $C$ is a line bundle, or a direct sum of copies of a line bundle.