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Is there a source in which Demazure's function $p$ defined in SGA3, exp. XXI, is calculated?

Suppose that $mathcal{R}=(M,R,M^*,R^*)$ is a root datum. In section 1.2 of SGA3, exp. XXI, Demazure defines the $mathbb Z$-linear map $p:Mto M^*$ by$$p(x)=sum_{uin R^*}(u,x)u$$and...

Asked on 12/15/2021 by inkspot

0 answer

Potential p-norm on tuples of operators

Consider $left[begin{matrix}A \ Bend{matrix}right] in B(H)^2$. One can define$$left|left[begin{matrix}A \ Bend{matrix}right]right|_p = | |A|^p + |B|^p|^{1/p}.$$ Q: Is this a norm? Consider the matrices ...

Asked on 12/15/2021 by Chris Ramsey

1 answer

Understanding a quip from Gian-Carlo Rota

In the chapter "A Mathematician's Gossip" of his renowned Indiscrete Thoughts, Rota launches into a diatribe concerning the "replete injustice" of misplaced credit and "forgetful hero-worshiping" of the mathematical community....

Asked on 12/13/2021 by William Stagner

5 answer

What is Chemlambda? In which ways could it be interesting for a mathematician?

I${}^{*}$ have randomly come across a couple of websites (Chemlambda project, chorasimilarity) that seem to be about a certain "thing" (a computer program, I think) called...

Asked on 12/13/2021

1 answer

Degree inequality of a polynomial map distinguishing hyperplanes

Let $H_1, ldots, H_n$ be $n$ linearly independent hyperplanes in $k^n$, for some arbitrary field $k$. Let $X = H_1 cup H_2 cup cdots cup...

Asked on 12/13/2021

1 answer

The inconsistency of Graham Arithmetics plus $ forall n, n < g_{64}$

As you all know, Ronald Graham just passed away. He is famous for many fabulous contributions to finite combinatorics, and much much more, but perhaps none of them is...

Asked on 12/13/2021 by Mirco A. Mannucci

2 answer

Subgraph induced by negative cycles detected by Bellman-Ford algorithm

What is known about the properties of the subgraph induced by the negative cycles are defined by the predecessor relation that is established during the execution of the Bellman-Ford algorithm...

Asked on 12/13/2021

0 answer

How to obtain matrix from summation inverse equation

I have a set of square matrices ${A_i}_{i in {1,..., n}}$ and another square matrix of equal size $K$. Under the assumption that such a matrix exists and...

Asked on 12/13/2021 by JDoe2

1 answer

Is $arcsin(1/4) / pi$ irrational?

Is $arcsin(1/4) / pi$ rational? An approximation given by a calculator seem to suggest that it isn't, but I found no proof. Thanks in advance!...

Asked on 12/13/2021 by ikp

3 answer

A mutliplication for distributive lattices via rowmotion

Let $L$ be a finite distributive lattice. In case $L$ is Boolean one can define a multiplication by $a*b:=(a cup b) setminus (a cap b)=(a cup b)...

Asked on 12/13/2021

0 answer

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