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The LGV lemma does not really require nodes to lie in a plane. In fact the statement is very simple without any geometric assumptions on the nodes. The role of the spatial arrangement of nodes is usua …

No for $n\geq 3$. If $A\in M_n(\mathbf Z_p)$ were similar to $A^T\in M_n(\mathbf Z_p)$, then going modulo $p^2$, its image in $M_n(\mathbf Z/p^2\mathbf Z)$ would be similar to the image of its transp …

This is answered in Theorem 4 of my paper Comparison of Gelfand-Tsetlin Bases for Alternating and Symmetric Groups, with Geetha Thangavelu, which is published in Algebras and Representation Theory, an …

Define a standard bitableau of size $n$ to be a pair $(P_1, P_2)$ of standard tableaux of total size $n$ such that each of the integers $1,\dotsc, n$ occurs exactly once in either tableau. Then $I_2( …

One way to see this is to note that $T$ splits from any locally compact abelian group (D.L. Armacost, The Structure of Locally Compact Abelian Groups, 6.16). If the cocycle is commutative, then the as …

Jeff Adams has comprehensive notes on his website: http://www.math.umd.edu/~jda/characters/characters.pdf The irreducible characters of the groups SL(2), PGL(2), GL(2) and PSL(2) over finite fields a …

In the OEIS entry for Bell numbers, there appears a generating function $$\sum_{k=0}^\infty B_k t^k = \sum_{r=0}^\infty \prod_{i=1}^r \frac{t}{1-it}$$ However, I could not locate any proof of refere …

I quote from one of my papers (On Bernstein's presentation of Iwahori-Hecke algebras and representations of split reductive groups over non-Archimedean local fields, Bulletin of the Kerala Mathematics …

A group is said to be a $Q$-group if the character of any complex representation is rational valued. A well-known internal characterization of $Q$-groups is the following: $G$ is a $Q$-group if an …

A nice set of generators for the automorphism group of a finite abelian group is described by Garrett Birkhoff in his paper titled "Subgroups of abelian groups", Proc. London Math. Soc., s2-38(1):385- …

It's all written up rather nicely in Heather Dornom's Honours thesis from 2005. She gives a version of the matrix ball construction that works in these cases and also explains growth models for the RS …

Is a geometric construction of the dual RSK correspondence along the lines of Viennot's "light and shadows construction" written up somewhere? This is a bijective correspondence between 0-1 matrices a …

The RS correspondence is a correspondence which associates to each permutation a pair of standard Young tableaux of the same shape. The RSK correspondence associates to each integer matrix (with non- …

Besides the basic definitions and examples, you will find a concise description of the vocabulary needed to talk about linear algebraic groups over fields that are not algebraically closed in T. A. Sp …

In my opinion, the beginner would find the following very helpful: MacDonald's book, spherical functions on a group of p-adic type (out of print) Joseph Rabinoff's senior thesis at Harvard. It's a v …