By Mathieu O., Papadopoulo G.
Enable ok be an algebraically closed box of finite attribute p, and permit be an integer. within the paper, we supply a personality formulation for all basic rational representations of with optimum weight any a number of of any primary weight. Our formulation is just a little extra normal: say dominant weight λ is specified if there are integers such that and . certainly, we compute the nature of any basic module whose maximum weight λ will be written as with every are particular. via stabilization, we get a personality formulation for a relations of irreducible rational -modules.
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Additional resources for A character formula for a family of simple modular representations of GL(n)
It had been weeks since I’d been inside the home, and it was not as I remembered it. I gaped at the squalor. I stood stifled against a counter in the kitchen that a few months earlier I’d cleaned and organized from top to bottom. Now the contents of the cupboards had been yanked unceremoniously from their nesting places, strewn haphazardly in heaps on the counters and floor. Like a giant petri dish, the aluminum sink held stacks of dirty dishes in a puddle of stagnant water. Shards of glass glistened in the spoiled food that clung to the plates and silverware.
I was an emotional mess before I met my first husband, then after what he did to me, I was even worse. I was only 16 years old; I had no business being a mother. I was too young, too immature, and too unstable. But, oh, how I loved my son. You may argue that babies have been having babies for centuries. It wasn’t unusual in many cultures for girls to leave their homes as young as age 13 to begin families. However, in most of these instances, the babies were raised in households where extended family resided.
I was just in her shop to order something, and an hour later we were still talking, but about her life, not my reason for being there in the first place. Then again, perhaps that’s exactly why I was there in the first place. God has a way of orchestrating divine appointments. She went on to talk about her own parents—how cruel her mother had been to her when she was young, and how she vowed never to treat her children the same way. So then I asked, “What’s cruel about defining your boundaries and teaching your children right from wrong?