TY - JOUR AU - Bonnafé, Cédric PY - 2018/12/31 Y2 - 2024/03/29 TI - Blocks of the Grothendieck Ring of Equivariant Bundles on a Finite Group JF - New Zealand Journal of Mathematics JA - NZ J Math VL - 48 IS - 0 SE - Articles DO - 10.53733/29 UR - https://www.nzjmath.org/index.php/NZJMATH/article/view/29 SP - 157-163 AB - <p>If <span class="texhtml"><em>G</em></span> is a finite group, the Grothendieck group <img class="tex" src="http://nzjm.math.auckland.ac.nz/images/math/8/6/f/86f97d365f8314c3728a3711abfb5d42.png" alt="\mathbf{K}_G(G)"> of the category of <span class="texhtml"><em>G</em></span>-equivariant <img class="tex" src="http://nzjm.math.auckland.ac.nz/images/math/f/0/b/f0b01fe0a1eec87c634584ac0694fb71.png" alt="\mathbb{C}">-vector bundles on <span class="texhtml"><em>G</em></span> (for the action of <span class="texhtml"><em>G</em></span> on itself by conjugation) is endowed with a structure of (commutative) ring. If <span class="texhtml"><em>K</em></span> is a sufficiently large extension of <img class="tex" src="http://nzjm.math.auckland.ac.nz/images/math/1/1/3/1135f2d0019ceb7752fd7dbad77ebf7f.png" alt="\mathbb{Q}_{\! p}"> and <img class="tex" src="http://nzjm.math.auckland.ac.nz/images/math/a/e/b/aeb29ed2e1ec2353da1748944aef3c2f.png" alt="\mathcal{O}"> denotes the integral closure of <img class="tex" src="http://nzjm.math.auckland.ac.nz/images/math/3/5/8/35802092ca5aa786e83b5dd5f815bb0c.png" alt="\mathbb{Z}_{\! p}"> in <span class="texhtml"><em>K</em></span>, the <span class="texhtml"><em>K</em></span>-algebra <img class="tex" src="http://nzjm.math.auckland.ac.nz/images/math/f/d/3/fd3628b77748250b62f305a25ab481c8.png" alt="K\mathbf{K}_G(G)=K \otimes_\mathbb{Z} \mathbf{K}_G(G)"> is split semisimple. The aim of this paper is to describe the <img class="tex" src="http://nzjm.math.auckland.ac.nz/images/math/a/e/b/aeb29ed2e1ec2353da1748944aef3c2f.png" alt="\mathcal{O}">-blocks of the <img class="tex" src="http://nzjm.math.auckland.ac.nz/images/math/a/e/b/aeb29ed2e1ec2353da1748944aef3c2f.png" alt="\mathcal{O}">-algebra <img class="tex" src="http://nzjm.math.auckland.ac.nz/images/math/0/a/5/0a5ce418acc91daa3ea8e2fb843dfafb.png" alt="\mathcal{O}\mathbf{K}_G(G)">.</p> ER -