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Comments to 1998-002-09

Comments on article:
G. Lusztig; Errata to Bases in equivariant K-theory Represent. Theory 2 (1998), pp. 298-369.

Added September 29, 1999 17:01:45 EDT

Comments by the author


These errata are available in the following formats:

Return to abstract: gif

2.18, line 2: delete ``the equality ${}^{\sigma _{i}}\rho =\rho -\alpha _{i}$"

3.8(b): replace $n<n_{0}$ by $n>n_{0}$

p.314, line 4: replace $[x]m,[x]\tilde m,[x']m',[x']\tilde m'$ by ${}_{\iota }m, {}_{\iota }\tilde m, {}_{\iota '} m', {}_{\iota '}\tilde m'$

3.14(b): replace $\tilde b$ by $\tilde {\hat b}$

3.14(c): replace $b$ by $\hat b$

p.315, line -2,-1: replace $\Pi '$ by $\Pi $

p.315, line -1: replace last $=$ by $\in $

p.316, line 3: replace last $=$ by $\in $

p.316, line 7: insert $)$ after $\mathcal{A}$

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 $\pi _{12},\pi _{23},\pi _{13}$

7.9(a): replace $p_{12},p_{13},p_{23}$ by $\pi _{12},\pi _{13}, \pi _{23}$

7.14, line 2: replace $\Lambda ^{2}$ by $\Lambda \times \mathcal B$

7.16, line 4: replace ``line bundle" by ``vector bundle"

7.18(a): replace $v$ by $v^{2}$

7.19, last line: replace $\mathbf Z_{i}$ by $\overline{Z}_{i}$

7.23, 7.24, 7.25: replace $\tilde T_{i}$ by $\tilde T_{\sigma _{i}}$

8.3,8.4: replace $s_{i}$ by $\sigma _{i}$

8.4, line 1,2: replace $h:Z_{w}\to Z_{\le w}$ by $h:Z_{\le w}\to Z_{w}$

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 $K_{\mathcal{G}}$

8.11: line 4 of proof; replace $v\xi $ by $v\xi '$

8.11: last line of proof; replace 10.1 by 8.10

9.7, line 1: replace $D'(\xi 0$ by $D'(\xi )$

p.343, line -3: replace $Z_{0}=\{(y,\mathfrak b)\in \Lambda |\mathfrak b'=\mathfrak b_{0}\}$ by $Z_{0}=\{(y,\mathfrak b)\in \Lambda |y\in \mathfrak n_{0}\}$

10.6, line -5: the last arrow should have a $\sim $ on top

10.8, 10.10, 10.11, 10.12: replace $g,\tilde g$ by $g^{-1},\tilde g^{-1}$

10.10, line 2: replace $L_{x'}$ by $L_{x}$

11.3, line 3: replace $(0,\mathfrak b)$ by $(e,\mathfrak b)$

11.3: replace $\lim _{t\to 0}$ by $\lim _{\lambda \to 0}$

11.3: replace $\lim _{t\to \infty }$ by $\lim _{\lambda \to \infty }$

11.4(a): replace $\mathcal B_{e,\mu }^{\mathbf C^{*}}$ by $\mathcal B_{e,\mu }$

11.4(b): replace $\Lambda _{e,\mu }^{\mathbf C^{*}}$ by $\Lambda _{e,\mu }$

11.10: replace $Vec_{\Lambda _{e}}$ by $Vec_{H}(\Lambda _{e})$

11.10 (last line): replace $2\dim \mathfrak g/\mathfrak z(f)$ by $\dim \mathfrak g/\mathfrak z(f)$ (twice)

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

12.9: replace first two sentences by: ``Let $d(e)=(1/2)\dim \text {\rm Ad}(G)e$."

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 $\varpi $ is uniquely defined by $e,f,h,C$ up to conjugation by $\text {\rm Ad}(c)$ where $c\in C$.

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