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... | [{"type": "text", "text": "The Automorphisms of Affine Fusion Rings ", "text_level": 1, "page_idx": 0}, {"type": "text", "text": "Terry Gannon ", "page_idx": 0}, {"type": "text", "text": "Department of Mathematical Sciences, University of Alberta, Edmonton, Canada, T6G 2G1 e-mail: tgannon@math.ualberta.ca ", "page_idx"... | {"preproc_blocks": [{"type": "title", "bbox": [140, 66, 471, 87], "lines": [{"bbox": [141, 69, 469, 88], "spans": [{"bbox": [141, 69, 469, 88], "score": 1.0, "content": "The Automorphisms of Affine Fusion Rings", "type": "text"}], "index": 0}], "index": 0}, {"type": "text", "bbox": [260, 115, 351, 129], "lines": [{"bbo... | {"layout_dets": [{"category_id": 1, "poly": [196, 1136, 1504, 1136, 1504, 1453, 196, 1453], "score": 0.986}, {"category_id": 1, "poly": [197, 886, 1505, 886, 1505, 1135, 197, 1135], "score": 0.985}, {"category_id": 1, "poly": [195, 1705, 1504, 1705, 1504, 1826, 195, 1826], "score": 0.978}, {"category_id": 1, "poly": [1... | # The Automorphisms of Affine Fusion Rings
Terry Gannon
Department of Mathematical Sciences, University of Alberta, Edmonton, Canada, T6G 2G1 e-mail: tgannon@math.ualberta.ca
arXiv:math/0002044v1 [math.QA] 7 Feb 2000
# 1. Introduction
Verlinde’s formula [33]
$$
V_{a^{1}\ldots a^{t}}^{(g)}=\sum_{b\in\Phi}(S_{0b}... | <div class="pdf-page">
<h1>The Automorphisms of Affine Fusion Rings</h1>
<p>Terry Gannon</p>
<p>Department of Mathematical Sciences, University of Alberta, Edmonton, Canada, T6G 2G1 e-mail: tgannon@math.ualberta.ca</p>
<h1>1. Introduction</h1>
<p>Verlinde’s formula [33]</p>
<p>arose first in rational conformal field th... | <div class="pdf-page">
<h1 class="pdf-title" data-x="234" data-y="85" data-width="554" data-height="27">The Automorphisms of Affine Fusion Rings</h1>
<p class="pdf-text" data-x="435" data-y="148" data-width="152" data-height="18">Terry Gannon</p>
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... | [{"type": "text", "text": "The point of introducing the $N_{a b}^{c}$ in (1.1b) is that they define an algebraic structure, the fusion ring. Consider all formal linear combinations of objects $\\chi_{a}$ labelled by the $a\\in\\Phi$ ; the multiplication is defined to have structure constants $N_{a b}^{c}$ : ", "page_id... | {"preproc_blocks": [{"type": "text", "bbox": [70, 70, 541, 115], "lines": [{"bbox": [93, 73, 540, 89], "spans": [{"bbox": [93, 73, 249, 89], "score": 1.0, "content": "The point of introducing the ", "type": "text"}, {"bbox": [249, 75, 268, 88], "score": 0.93, "content": "N_{a b}^{c}", "type": "inline_equation", "height... | {"layout_dets": [{"category_id": 1, "poly": [198, 685, 1504, 685, 1504, 1321, 198, 1321], "score": 0.985}, {"category_id": 1, "poly": [197, 482, 1502, 482, 1502, 683, 197, 683], "score": 0.984}, {"category_id": 1, "poly": [197, 1541, 1502, 1541, 1502, 1663, 197, 1663], "score": 0.97}, {"category_id": 1, "poly": [197, 1... | The point of introducing the in (1.1b) is that they define an algebraic structure, the fusion ring. Consider all formal linear combinations of objects labelled by the ; the multiplication is defined to have structure constants :
$$
\chi_{a}\chi_{b}=\sum_{c\in\Phi}N_{a b}^{c}\chi_{c}
$$
As an abstract ring, it is... | <div class="pdf-page">
<p>The point of introducing the in (1.1b) is that they define an algebraic structure, the fusion ring. Consider all formal linear combinations of objects labelled by the ; the multiplication is defined to have structure constants :</p>
<p>As an abstract ring, it is not so interesting (the fu... | <div class="pdf-page">
<p class="pdf-text" data-x="117" data-y="90" data-width="788" data-height="58">The point of introducing the in (1.1b) is that they define an algebraic structure, the fusion ring. Consider all formal linear combinations of objects labelled by the ; the multiplication is defined to have structu... | {
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# 2.1. The affine fusion ring
The source of some of the most interesting fusion data are the affine nontwisted Kac-Moody algebras [23]. Choose any positive integer . Consider the (finite) set of level integrable highest weights:
$$
P_{+}\stackrel{\mathrm{def}}{=}\{\sum_{j=0}^{r}\lambda_{j}\Lambd... | <div class="pdf-page">
<h1>2.1. The affine fusion ring</h1>
<p>The source of some of the most interesting fusion data are the affine nontwisted Kac-Moody algebras [23]. Choose any positive integer . Consider the (finite) set of level integrable highest weights:</p>
<p>where denote the fundamental weights, and ... | <div class="pdf-page">
<div class="pdf-discarded" data-x="428" data-y="91" data-width="164" data-height="18" style="opacity: 0.5;">2. Generalities</div>
<h1 class="pdf-title" data-x="117" data-y="129" data-width="241" data-height="20">2.1. The affine fusion ring</h1>
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