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Selecta Mathematica

, Volume 20, Issue 4, pp 1247–1248 | Cite as

Erratum to: Formal Hecke algebras and algebraic oriented cohomology theories

  • Alex Hoffnung
  • José Malagón-López
  • Alistair Savage
  • Kirill Zainoulline
Erratum

1 Erratum to: Sel. Math. New Ser. DOI 10.1007/s00029-013-0132-8

Proposition 6.8(d) contains a few sign errors. We thank Marc-Antoine Leclerc for bringing this to our attention. The correct statement is as follows:

If \(\langle \alpha _i^\vee , \alpha _j \rangle =-1\) and \(\langle \alpha _j^\vee , \alpha _i \rangle =-3\) so that \(m_{ij}=6\), then
$$\begin{aligned}&\varDelta _{jijiji}- \varDelta _{ijijij}\nonumber \\&\quad = \varDelta _{ijij} (\kappa _{j,i} + \kappa _{2i+3j,-i-2j} + \kappa _{-i-3j,i+2j} + \kappa _{i+2j,-j})\nonumber \\&\qquad - \varDelta _{jiji} (\kappa _{i,j} + \kappa _{-2i-3j,i+2j} + \kappa _{-i-2j,i+3j} + \kappa _{i+j,j})\nonumber \\&\qquad + \varDelta _{jij} \big ( \Delta _i (\kappa _{i,j} + \kappa _{-2i-3j,i+2j} + \kappa _{-i-2j,i+3j} + \kappa _{i+j,j}) \big )\nonumber \\&\qquad - \varDelta _{iji} \big ( \Delta _j (\kappa _{j,i} + \kappa _{2i+3j,-i-2j} + \kappa _{-i-3j,i+2j} + \kappa _{i+2j,-j}) \big )\nonumber \\&\qquad + \varDelta _{ij} \xi _{ij} - \varDelta _{ji} \xi _{ji} + \varDelta _j (\Delta _i(\xi _{ji})) - \varDelta _i (\Delta _j(\xi _{ij})) \end{aligned}$$
(6.8)
where
$$\begin{aligned} \xi _{ij}&= \tfrac{1}{x_i x_{i+j} x_{i+2j} x_{2i+3j}} + \tfrac{1}{x_ix_jx_{i+2j}x_{-2i-3j}} + \tfrac{1}{x_ix_jx_{2i+3j}x_{-i-j}} - \tfrac{1}{x_ix_{i+j}x_{i+2j}x_{-i-3j}} \\&-\, \tfrac{1}{x_ix_{i+j}x_{i+3j}x_{-j}} + \tfrac{1}{x_{i+j}x_{i+3j}x_{-j}x_{-2i-3j}} + \tfrac{1}{x_{i+3j}x_{2i+3j}x_{-j}x_{-i-2j}} \\&+\,\tfrac{1}{{x_{i+j}x_{i+2j}x_{-i-3j}x_{-2i-3j}}} - \tfrac{1}{x_ix_jx_{i+2j}x_{i+3j}} \end{aligned}$$
and
$$\begin{aligned} \xi _{ji}&= \tfrac{1}{x_ix_jx_{2i+3j}x_{-i-2j}} + \tfrac{1}{x_ix_jx_{i+2j}x_{-i-3j}} + \tfrac{1}{x_jx_{i+2j}x_{i+3j}x_{2i+3j}} - \tfrac{1}{x_ix_jx_{i+j}x_{2i+3j}} \\&+\, \tfrac{1}{x_{i+j}x_{i+2j}x_{-i}x_{-2i-3j}} + \tfrac{1}{x_{i+3j}x_{2i+3j}x_{-i-j}x_{-i-2j}} + \tfrac{1}{x_{i+j}x_{i+3j}x_{-i}x_{-i-2j}} \\&- \,\tfrac{1}{x_j x_{i+3j}x_{2i+3j}x_{-i-j}} - \tfrac{1}{x_jx_{i+j}x_{i+3j}x_{-i}}. \end{aligned}$$

Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Alex Hoffnung
    • 1
    • 3
  • José Malagón-López
    • 2
    • 3
  • Alistair Savage
    • 3
  • Kirill Zainoulline
    • 3
  1. 1.Temple University, Dept. of MathematicsPhiladelphiaUSA
  2. 2.University of Toronto Mississauga, Department of Mathematics and Computational SciencesMississaugaCanada
  3. 3.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada

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