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On the extended Catalan arrangement of type $B_\ell$

Hiraku Kawanoue

Abstract

We give an explicit formula for the generators of the logarithmic vector field of the coning of the extended Catalan arrangement of type $B_\ell$.

On the extended Catalan arrangement of type $B_\ell$

Abstract

We give an explicit formula for the generators of the logarithmic vector field of the coning of the extended Catalan arrangement of type .

Paper Structure

This paper contains 5 sections, 8 theorems, 55 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The case $\ell=1$
  4. The case $\ell>1$.
  5. Proof of the main theorem

Key Result

Theorem 1

The set $\{\delta_E\}\cup \{\delta_{\ell,m,u}\mid u=0,1,\dotsc,\ell-1\}$ forms a basis of $D(c\!\,\operatorname{Cat}(B_\ell,m))$.

Theorems & Definitions (13)

  • Theorem 1
  • Corollary 2
  • Proposition 3
  • proof
  • Lemma 4
  • proof
  • Proposition 5
  • proof
  • Lemma 6
  • proof
  • ...and 3 more