ERRATA TO “BASES IN EQUIVARIANT K-THEORY”

G. LUSZTIG

2.18, line 2: delete “the equality ^{σ_{i}}ρ = ρ − α_{i}” 3.8(b): replace n < n_{0} by n > n_{0} p.314, line 4: replace [x]m, [x]m̃, [x′]m′, [x′]m̃′ by _{ι}m,_{ι}m̃,_{ι′}m′,_{ι′}m̃′ 3.14(b): replace b̃ by ˜ b̂ 3.14(c): replace b by b̂ p.315, line -2,-1: replace Π′ by Π p.315, line -1: replace last = by ∈ p.316, line 3: replace last = by ∈ p.316, line 7: insert ) after A 5.2(a): replace , by : 5.17: replace “We apply the identity 5.15(a) with” by “Let” 5.17: replace “as in the proof of 5.15” by “as in the proof of 5.14” 7.9, line 5: replace p_{12}, p_{13}, p_{23} by π_{12}, π_{23}, π_{13} 7.9(a): replace p_{12}, p_{13}, p_{23} by π_{12}, π_{13}, π_{23} 7.14, line 2: replace Λ^{2} by Λ × B 7.16, line 4: replace “line bundle” by “vector bundle” 7.18(a): replace v by v^{2} 7.19, last line: replace Z_{i} by \overline{Z}_{i} 7.23, 7.24, 7.25: replace T̃_{i} by T̃_{σ_{i}} 8.3,8.4: replace s_{i} by σ_{i} 8.4, line 1,2: replace h : Z_{w} → Z_{≤w} by h : Z_{≤w} → Z_{w} p.337, line 1: delete and replace by “We have” p.337, line 2: replace k^{∗} by h^{∗} 8.7, line 2: replace Z_{w} by Z_{w′} 8.7(b): replace the last K by K_{G} 8.11: line 4 of proof; replace vξ by vξ′ 8.11: last line of proof; replace 10.1 by 8.10 9.7, line 1: replace D′(ξ0 by D′(ξ) p.343, line -3: replace Z_{0} = {(y, 𝔟) ∈ Λ|𝔟′ = 𝔟_{0}} by Z_{0} = {(y, 𝔟) ∈ Λ|y ∈ 𝔫_{0}} 10.6, line -5: the last arrow should have a ∼ on top 10.8, 10.10, 10.11, 10.12: replace g, g̃ by g^{−1}, g̃^{−1} 10.10, line 2: replace L_{x′} by L_{x} 11.3, line 3: replace (0, 𝔟) by (e, 𝔟) 11.3: replace lim_{t→0} by lim_{λ→0} 11.3: replace lim_{t→∞} by lim_{λ→∞} 11.4(a): replace B_{e,μ}^{C^{∗}} by B_{e,μ} 11.4(b): replace Λ_{e,μ}^{C^{∗}} by Λ_{e,μ} 11.10: replace V ec_{Λ_{e}} by V ec_{H}(Λ_{e}) 11.10 (last line): replace 2 dim 𝔤/𝔷(f) by dim 𝔤/𝔷(f) (twice)

12.1-12.4 replace by: Let e, f, h, C, 𝔠, H be as in 11.1. We can find an opposition ϖ of 𝔤 such that ϖ(e) = −e, ϖ(f) = −f, ϖ(h) = h and ϖ = −1 on 𝔠. We fix such a ϖ.

12.9: replace first two sentences by: “Let d(e) = (1/2) dim Ad(G)e.” 12.18 (beginning) add: Let L be the centralizer of C in G. In the remainder of

this paper we assume that the centralizer of e, f, g in L is equal to the centre of L. Then ϖ is uniquely defined by e, f, h, C up to conjugation by Ad(c) where c ∈ C.

14.2–14.5: replace by the revision in [L7, 2.4] or by 17.2 in this paper.