• Korean Journal of Mathematics
• /
• v.22 no.2
• /
• pp.325-337
• /
• 2014

In 1911 Schur[6] derived degree and character formulas for projective representations of the symmetric groups remarkably similar to the corresponding formulas for ordinary representations. Morris[3] derived a recurrence for evaluation of spin characters and Stembridge[8] gave a combinatorial reformulation for Morris' recurrence. In this paper we give combinatorial interpretations for the orthogonality relations of spin characters based on Stembridge's combinatorial reformulation for Morris' rule.

• Bulletin of the Korean Chemical Society
• /
• v.34 no.12
• /
• pp.3777-3781
• /
• 2013

A formal total synthesis of aliskiren was accomplished. A key in our synthesis was to use the symmetric ciscisoid-cis-bis-lactone 3' as a precursor, which was prepared from D-tartrate diester. Appending the end groups and functional group transformations completed the synthesis.

• Korean Journal of Mathematics
• /
• v.19 no.4
• /
• pp.409-421
• /
• 2011

We study a natural map from the braid group to the mapping class group which is called Harer map. It is rather new and different from the classical map which was studied in 1980's by F. Cohen, J. Harer et al. We show that this map is homologically trivial for most coefficients by using the fact that this map factors through the symmetric group.

• Kyungpook Mathematical Journal
• /
• v.45 no.4
• /
• pp.561-570
• /
• 2005

Weak Crossed Product Algebras correspond to certain graphs called lower subtractive graphs. The properties of such algebras can be obtained by studying this kind of graphs ([4], [5]). In [1], the author showed that a weak crossed product is Frobenius and its restricted subalgebra is symmetric if and only if its associated graph has a unique maximal vertex. A special construction of these graphs came naturally and was known as standard lower subtractive graph. It was a deep question that when such a special graph possesses unique maximal vertex? This work is to answer the question partially and to give a particular characterization for such graphs at which the corresponding algebras are isomorphic. A graph that follows the mentioned characterization is called flexible. Flexibility is to some extend a generalization of the so-called Coxeter groups and its weak Bruhat ordering.

• East Asian mathematical journal
• /
• v.33 no.1
• /
• pp.45-52
• /
• 2017

Motivated by the problem of determining all right ideals of a group algebra FG for a finite group G over a finite field F, we explicitly determine the faithful irreducible representations of some finite metacylic groups over finite fields. By using that result, we determine the structure of all right ideals of the group algebra for the symmetric group $S_3$ over a finite field F, as an example.

• Bulletin of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.509-518
• /
• 1997

In this paper, we study the developing maps of the Lie groups with left-invariant affinely flat structures. We make some bacis observations on the nature of the developing images and show that the developing map for an incomplete affine structure splits as a product of a covering map of codimension 1 and a diffeomorphism of dimension 1.

• Journal of the Korean Mathematical Society
• /
• v.40 no.2
• /
• pp.179-193
• /
• 2003

The braid-permutation group is a group of welded braids which is the extension of Artin's braid groups by the symmetric groups. It is also described as a subgroup of the automorphism group of a free group. We also show that the plus-construction of the classifying space of the infinite braid-permutation group has the following two types of splittings BBP(equation omitted) B∑(equation omitted) $\times$ X, BBP(equation omitted) B $^{＋}$$\times$ Y＝S$^1$$\times$Y, where X, Y are some spaces.

• Communications of the Korean Mathematical Society
• /
• v.21 no.1
• /
• pp.151-163
• /
• 2006

Any simply connected fixed point cohomogeneity one riemannian manifold with positive sectional curvature is diffeomorphic to one of the compact rank one symmetric spaces.

• Journal of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.345-370
• /
• 1997

In this paper, we introduce the Fock representation $U^{F, M}$ of the Heisenberg group $H_R^(g, h)$ associated with a positive definite symmetric half-integral matrix $M$ of degree h and prove that $U^{F, M}$ is unitarily equivalent to the Schrodinger representation of index $M$.

• Bulletin of the Korean Chemical Society
• /
• v.30 no.2
• /
• pp.287-288
• /
• 2009