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$B_n$ �� Weyl Ⱥ��ĳЩ $sl_2$ �ͱ�ʾ\\
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�մ���\\
����˹������ѧ\\
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������, ����˹�� 66506\\
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ժҪ 
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���������� Coxeter ���͵�һЩ�Ӹ���, �������ά����ͬ��ģ
���ֽ�ɲ���Լ�� $W$-��ģ, ���� $W$ Ϊ�йص� Weyl Ⱥ��
�˷ֽ�ķ����Ǻ��������, ��Ϊ��Ӧ�ı�ԭ�ݵ�Ԫ�صĹ�����
��������� $sl_2({\bf C})$  �Ĳ���Լ�ı�ʾ������

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\noindent�ؼ���: Tits ����, Coxeter  ����, ����ѡ��ĸ���,
��ԭ�ݵ�Ԫ�ء�

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         {\bf $sl_2$-Type Representations of the Weyl Group of Type $B_n$}
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Su Dawei (David B. Surowski)\\
Department of Mathematics \\
Kansas State University\\      
Manhattan, KS 66506, U.S.A.
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{\sf Abstract}
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In this paper, certain rank selected subcomplexes of the Coxeter
complex (corresponding to $B_n$ or $C_n$ type Coxeter groups) are
introduced and the top homology modules are decomposed into
irreducible $W$-submodules, where $W$ is the relevant Weyl group.

The method of decomposition is of interest because the constructions of
the affording primitive idempotents are quite reminiscient of the           
irreducible polynomial representations of the complex Lie Algebra
$sl_2({\bf C})$.

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\noindent {\sf Key Words:} {\em Tits complex, Coxeter complex, rank-
selected subcomplex, primitive idempotents.}



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