Selecta Mathematica

, Volume 20, Issue 4, pp 1247–1248

# 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}

## Authors and Affiliations

• Alex Hoffnung
• 1
• 3
• José Malagón-López
• 2
• 3
• Alistair Savage
• 3
Email author
• 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